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Quantum Effects379?minutes370?marksQ1.????????? (a)???? (i)????? Explain the meaning of the term?work function?of a metal........................................................................................................................................................................................................................................................................................................................................(ii)???? State what you would need to change in an experiment to investigate the effect of the work function on the photoelectric effect..............................................................................................................(3)(b)???? Experiments based on the photoelectric effect support the particle theory of light. Stateone?conclusion drawn from these experiments and explain how it supports the particle theory.You may be awarded marks for the quality of written communication in your answer.....................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(2)(c)???? Monochromatic light of wavelength 4.80 × 10–7?m falls onto a metal surface which has a work function of 1.20 × 10–19?J.Calculate(i)????? the energy, in J, of a single photon of this light,.................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(ii)???? the maximum kinetic energy, in J, of an electron emitted from the surface..................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(5)(Total 10 marks)??Q2.????????? The diagram shows four energy levels of an atom not drawn to scale.(a)???? (i)????? Explain how this atom emits a line spectrum following excitation.You may be awarded marks for the quality of written communication in your answer..................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(ii)???? The longest wavelength of emitted radiation is produced by a transition between which two levels?.............................................................................................................(iii)???? Draw on the diagram?two?vertical arrows between levels to indicate two different transitions that result in emitted radiation of the same frequency.(4)(b)???? In its ground state the atom absorbs 2.3 × 10–19?J of energy from a collision with an electron.(i)????? Calculate all the possible frequencies of radiation that the atom may subsequently emit...............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(ii)???? How much energy, in eV, would be required to ionise the atom in its ground state?..........................................................................................................................................................................................................................(5)(Total 9 marks)??Q3.????????? Electrons travelling at a speed of 5.00 × 105?m s–1?exhibit?wave properties.(a)???? What phenomenon can be used to demonstrate the wave properties of electrons? Details of any apparatus used are not required.......................................................................................................................(1)(b)???? Calculate the wavelength of these electrons.........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(2)(c)???? Calculate the speed of muons with the same wavelength as these electrons.Mass of muon = 207 × mass of electron........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(3)(d)???? Both electrons and muons were accelerated from rest by the same potential difference. Explain why they have different wavelengths.........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(2)(Total 8 marks)??Q4.????????? (a)???? Electrons behave in two distinct ways. This is referred to as the?duality of electrons.(i)????? State what is meant by the duality of electrons...........................................................................................................................................................................................................................(ii)???? Give?one?example of each type of behaviour of electrons...........................................................................................................................................................................................................................(3)(b)???? Calculate the speed of electrons that have a de Broglie wavelength of 1.70?×?10–10?m.........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(2)(Total 5 marks)??Q5.????????? The diagram shows some of the energy levels of the mercury atom.(a)???? When electrons collide with mercury atoms, the atoms may be?excited?or may be?ionised.Explain what is meant by(i)????? excitation,.......................................................................................................................................................................................................................................................................................................................................(ii)???? ionisation........................................................................................................................................................................................................................................................................................................................................(2)(b)???? Determine the lowest frequency of emitted radiation with reference to the energy levels in the diagram...............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(2)(Total 4 marks)??Q6.????????? The graph shows how the maximum kinetic energy,?Ek, of electrons emitted from the surface of metal A, varies with the frequency,?f, of the incident electromagnetic radiation.(a)???? Explain the meaning of the term?threshold frequency.............................................................................................................................................................................................................................................(2)(b)???? Calculate the work function of metal A,(i)????? in J,.......................................................................................................................................................................................................................................................................................................................................(ii)???? in eV...........................................................................................................................................................................................................................(3)(c)???? Metal A is exchanged for metal B. The work function of metal B is half that of metal A.Add a line to the graph above to show how the maximum kinetic energy of electrons emitted from metal B varies with frequency.(2)(d)???? At a fixed frequency of the incident radiation, the emitted electrons are collected and a current is recorded.State and explain a change that may be made to increase this current.You may be awarded marks for the quality of written communication in your answer.....................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(3)(Total 10 marks)??Q7.????????? A fluorescent light tube contains mercury vapour at low pressure. The tube is coated on the inside, and contains two electrodes.(a)???? Explain why the mercury vapour is at a low pressure.............................................................................................................................................................................................................................................(1)(b)???? Explain the purpose of the coating on the inside of the tube.You may be awarded marks for the quality of written communication in your answer.................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(3)(Total 4 marks)??Q8.??????????Electromagnetic waves and electrons have properties of both particles and waves.Explain what evidence there is to support this statement.Experimental details are not required.You may be awarded marks for the quality of written communication in your answer.................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(Total 6 marks)??Q9.??????????The diagram shows some energy levels, in eV, of an atom.Photons of specific wavelengths are emitted from these atoms when they are?excited?by collisions with electrons.You may be awarded marks for the quality of written communication in your answer.(a)???? Explain(i)????? what is meant by the process of excitation,....................................................................................................................................................................................................................................................................................................................................................................................................................................................(ii)???? why the emitted photons have specific wavelengths..................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(5)(b)???? One of the emitted photons has an energy of 9.92 × 10–19?J.(i)????? Calculate the wavelength of this photon.....................................................................................................................................................................................................................................................................................................................................................................................................................................................(ii)???? Determine which transition is responsible for this emitted photon........................................................................................................................................................................................................................................................................................................................................(iii)???? Draw an arrow on the energy level diagram above?to show the transition responsible for the emission of a photon with the shortest wavelength.(7)(Total 12 marks)??Q10.??????????In the apparatus shown, monochromatic ultraviolet radiation is incident on the surface of metal?X. Photoelectrons are emitted from?X?and are collected at electrode?Y.(a)???? Calculate the work function of?X, given that each photon in the incident radiation has 3.2?×?10–19?J of energy.The maximum kinetic energy possessed by a single photoelectron is 2.1 × 10–19?J...................................................................................................................................................................................................................................................................................................................................................................(3)(b)???? The source of the incident radiation is replaced with a new source. The wavelength of the radiation from the new source is half the wavelength of the original radiation.Calculate the maximum kinetic energy of the emitted photoelectrons...................................................................................................................................................................................................................................................................................................................................................................(3)(Total 6 marks)??Q11.????????? A?proton and an electron have the same velocity. The de Boglie wavelength of the electron is 3.2?×?10–8?m.(a)???? Calculate,(i)????? the velocity of the electron,....................................................................................................................................................................................................................................................................................................................................................................................................................................................(ii)???? the de Broglie wavelength of the proton........................................................................................................................................................................................................................................................................................................................................(4)(b)???? (i)????? State what kind of experiment would confirm that electrons have a wave-like nature. Experimental details are not required...........................................................................................................................................................................................................................(ii)???? State why it is easier to demonstrate the wave properties of electrons than to demonstrate wave properties of protons........................................................................................................................................................................................................................................................................................................................................(2)(Total 6 marks)??Q12.????????? (a)???? Explain what happens to electrons in hydrogen atoms when a spectrum, such as that represented below, is produced.You may be awarded marks for the quality of written communication in your answer...........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(4)(b)???? A fluorescent tube is normally coated on the inside with a powder. The tube is then filled with mercury vapour at low pressure. When the tube is switched on, the mercury vapour emits ultraviolet electromagnetic radiation.Explain how this ultraviolet radiation causes the powder to emit electromagnetic radiation as well. State the difference between the radiations emitted by the mercury vapour and the powder.You may be awarded marks for the quality of written?communication in your answer.......................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(4)(Total 8 marks)??Q13.????????? (a)???? The photoelectric effect is represented by the equationhf?=??+?Ek.What does?Ek?represent?............................................................................................................................................................................................................................................(2)(b)???? A metal plate is illuminated with electromagnetic radiation of wavelength 190 nm.The metal has a work function of 7.9 × 10–19?J.(i)????? Calculate the frequency of the incident electromagnetic radiation........................................................................................................................................................................................................................................................................................................................................(ii)???? Show that the metal plate will emit photoelectrons when illuminated with radiation of this wavelength.....................................................................................................................................................................................................................................................................................................................................................................................................................................................(iii)???? The radiation incident on the metal plate remains at a constant wavelength of 190?nm but its intensity is now doubled.State and explain the effect this has on the emitted photoelectrons.You may be awarded marks for the quality of written communication in your answer.........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(6)(Total 8 marks)??Q14.????????? The diagram shows some of the electron energy levels of an atom.An incident electron of kinetic energy 4.1 × 10–18?J and speed 3.0 × 106?m s–1?collides with?the atom represented in the diagram and excites an electron in the atom from level B?to?level D.(a)???? For the incident electron, calculate(i)????? the kinetic energy in eV,..........................................................................................................................................................................................................................(ii)???? the de Broglie wavelength.....................................................................................................................................................................................................................................................................................................................................................................................................................................................(4)(b)???? When the excited electron returns directly from level D to level B it emits a photon.Calculate the wavelength of this photon.....................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(3)(Total 7 marks)??Q15.????????? (a)???? Explain what is meant by the term?work?function?of a metal.............................................................................................................................................................................................................................................(2)(b)???? In an experiment on the photoelectric effect, the maximum kinetic energy of the emitted photoelectrons is measured over a range of incident light frequencies. The results obtained are shown in the figure below.(i)????? A metal of work function?Φ?is illuminated with light of frequency?f. Write down the equation giving the maximum kinetic energy,?EK, of the photoelectrons emitted in terms of?Φ?and?f.EK?=(ii)???? Use the data in the figure?to determine the work function of the metal.....................................................................................................................................................................................................................................................................................................................................................................................................................................................(iii)???? Determine the maximum kinetic energy of the photoelectrons when the frequency of the incident radiation is 2.5 × 1015?Hz.....................................................................................................................................................................................................................................................................................................................................................................................................................................................(6)(c)???? The experiment is repeated but with the light incident on a metal of lower work function. Draw a new line on the figure?that results from this change.(2)(Total 10 marks)??Q16.????????? Some energy levels of an atom of a gas are shown in?Figure 1.Figure 1When a current is passed through the gas at low pressure, a line spectrum is produced. Two of these lines, which correspond to transitions from levels B and C respectively to the ground state, are shown in?Figure 2.Figure 2(a)???? Describe what happens to an electron in an atom in the ground state in order for the atom to emit light of wavelength 4.0 × 10–7?m.You may be awarded marks for the quality of written communication in your answer.....................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(3)(b)???? Determine the energy, in J, of(i)????? the photons responsible for each of the two lines shown in?Figure 2,.................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(ii)???? levels B and C in?Figure 1........................................................................................................................................................................................................................................................................................................................................energy of level B = ...............................................................................energy of level C = ...............................................................................(5)(Total 8 marks)??Q17.??????????Some of the energy levels of an atom are shown below. The atom may be?ionised?by electron impact.energy/10–17?J0.00???? ______________________???????????? ionisation level–1.97?? ______________________???????????? level E–2.20?? ______________________???????????? level D–2.32?? ______________________???????????? level C–2.43?? ______________________???????????? level B–4.11?? ______________________???????????? level A (ground state)(a)???? (i)????? State what is meant by the ionisation of an atom...........................................................................................................................................................................................................................(ii)???? Calculate the minimum kinetic energy, in eV, of an incident electron that could ionise the atom from its ground state...........................................................................................................................................................................................................................(2)(b)???? You may be awarded marks for the quality of written communication in your answer to parts (b)(i) and (b)(ii).The atom in the ground state is given 5.00 × 10–17?J of energy by electron impact.(i)????? State what happens to this energy...........................................................................................................................................................................................................................(ii)???? Describe and explain what could happen subsequently to the electrons in the higher energy levels..................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(4)(c)???? Identify?two?transitions between energy levels that would give off electromagnetic radiation of the same frequency.__________ to __________and__________ to __________(2)(Total 8 marks)??Q18.????????? (i)????? A negative muon,??–, is 207 times more massive than an electron.Calculate the de Broglie wavelength of a negative muon travelling at 3.0?×?106?m?s–1...................................................................................................................................................................................................................................................................................................................................................................(ii)????? Using values from the data sheet calculate the ratio??where?π0?is a neutral pion...................................................................................................................................................................................................................................................................................................................................................................(iii)???? Calculate the speed necessary for a?π0?to have the same de Broglie wavelength as that of the??–?in part (i).........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(Total 6 marks)??Q19.????????? (a)???? One quantity in the photoelectric equation is a characteristic property of the metal that emits photoelectrons. Name and define this quantity...................................................................................................................................................................................................................................................................................................................................................................(2)(b)???? A metal is illuminated with monochromatic light. Explain why the kinetic energy of the photoelectrons emitted has a range of values up to a certain maximum.You may be awarded marks for the quality of written communication in your answer...........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(3)(c)???? A gold surface is illuminated with monochromatic ultraviolet light of frequency 1.8?×?1015?Hz. The maximum kinetic energy of the emitted photoelectrons is 4.2?×?10–19?J.Calculate, for gold,(i)????? the work function, in J,.................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(ii)???? the threshold frequency........................................................................................................................................................................................................................................................................................................................................(5)(Total 10 marks)??Q20.??????????Figure 1?shows the energy level diagram of a hydrogen atom. Its associated spectrum is shown in?Figure 2.The transition labelled?A?in?Figure 1?gives the spectral line labelled?B?in?Figure 2.Figure 1Figure 2hydrogen spectrum showing some of the main spectral lines(a)???? (i)????? Show that the frequency of spectral line B is about 4.6 × 1014?Hz........................................................................................................................................................................................................................................................................................................................................(ii)???? Calculate the wavelength represented by line B...........................................................................................................................................................................................................................(3)(b)???? The hydrogen atom is excited and its electron moves to level 4.(i)????? How many different wavelengths of electromagnetic radiation may be emitted as the atom returns to its ground state?.............................................................................................................(ii)???? Calculate the energy, in eV, of the longest wavelength of electromagnetic radiation emitted during this process...........................................................................................................................................................................................................................(2)(c)???? In a fluorescent tube, explain how the mercury vapour and the coating of its inner surface contribute to the production of visible light. You may be awarded additional marks to those shown in brackets for the quality of written communication in your answer...........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(3)(Total 8 marks)??Q21.????????? The apparatus shown in the figure below?can be used to demonstrate the photoelectric effect. Photoelectrons are emitted from the metal cathode when it is illuminated with white light which has passed through a blue filter.You may be awarded additional marks to those shown in brackets for the quality of written communication in your answers to parts (a) and (b).(a)???? The intensity of the light source is reduced. State and explain the effect of this on the emitted photoelectrons.........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(3)(b)???? Explain why no photoelectrons are emitted when the blue filter is replaced by a red filter.........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(3)(c)???? When a metal of work function 2.30 × 10–19?J is illuminated with ultraviolet radiation of wavelength 200 nm, photoelectrons are emitted.Calculate(i)????? the frequency of the ultraviolet radiation,..........................................................................................................................................................................................................................(ii)???? the threshold frequency of the metal,.......................................................................................................................................................................................................................................................................................................................................(iii)???? the maximum kinetic energy of the photoelectrons, in J.....................................................................................................................................................................................................................................................................................................................................................................................................................................................(5)(Total 11 marks)?Q22.????????? (a)???? When monochromatic light is incident on a metal plate, electrons are emitted only when the frequency of light exceeds a certain frequency.Explain in terms of energy, why this threshold frequency exists and why a photon theory of light provides a better explanation of the photoelectric effect than a wave theory of light.The quality of your written answer will be assessed in this question.............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(7)(b)???? A gold surface is illuminated with monochromatic ultra violet light of frequency2.10 × 1015?Hz. The maximum kinetic energy of an emitted photoelectron is6.20 × 10–19?J.Calculate(i)????? the energy, in J, of the incident photon,??energy = ..................................J(ii)???? the work function of gold,??work function = ....................................(5)(Total 12 marks)??Q23.????????? (a)???? State what is meant by the wave-particle duality of electrons...................................................................................................................................................................................................................................................................................................................................................................(1)(b)???? Electrons of wavelength 1.2 × 10–10?m are required to investigate the spacing between planes of atoms in a crystal.(i)????? Calculate the momentum of an electron of this wavelength stating an appropriate unit.???momentum of electron = ................................................(3)(ii)???? Calculate the speed of such an electron.???speed of electron = .............................................. m s–1(2)(iii)???? Calculate the kinetic energy of such an electron.???kinetic energy of electron = .................................................... J(2)(Total 8 marks)??Q24.????????? When light of a certain frequency is shone on a particular metal surface, electrons are emitted with a range of kinetic energies.(a)???? Explain???????? in terms of photons why electrons are released from the metal surface, and???????? why the kinetic energy of the emitted electrons varies upto a maximum value.????????? The quality of your written communication will be assessed in this question.........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(6)(b)???? The graph below shows how the maximum kinetic energy of the electrons varies with the frequency of the light shining on the metal surface.(i)????? On the graph mark the?threshold frequency?and label it?f0.(1)(ii)???? On the graph draw a line for a metal which has a higher threshold frequency.(2)(iii)???? State what is represented by the gradient of the graph..............................................................................................................(1)(c)???? The threshold frequency of a particular metal surface is 5.6 × 1014?Hz. Calculate the maximum kinetic energy of emitted electrons if the frequency of the light striking the metal surface is double the threshold frequency.??????answer = .................................. J(3)(Total 13 marks)??Q25.????????? The diagram below shows part of an energy level diagram for a hydrogen atom.????????? n = 4?_________________?–0.85 eVn = 3?_________________?–1.50 eVn = 2?_________________?–3.40 eV????????? n = 1?_________________?–13.60 eV(a)???? The level, n = 1, is the ground state of the atom.State the ionisation energy of the atom in eV.?answer = ................................... eV(1)(b)???? When an electron of energy 12.1 eV collides with the atom, photons of three different energies are emitted.(i)????? On the diagram above show with arrows the transitions responsible for these photons.(3)(ii)???? Calculate the wavelength of the photon with the smallest energy. Give your answer to an appropriate number of significant figures.???answer =.............................. m(5)(Total 9 marks)??Q26.????????? When monochromatic light is shone on a clean metal surface, electrons are emitted from the surface due to the photoelectric effect.(a)???? State and explain the effect on the emitted electrons of(i)????? increasing the frequency of the light,....................................................................................................................................................................................................................................................................................................................................................................................................................................................(2)(ii)???? increasing the intensity of the light.....................................................................................................................................................................................................................................................................................................................................................................................................................................................(2)(b)???? The wave model was once an accepted explanation for the nature of light. It was rejected when validated evidence was used to support a particle model of the nature of light. Explain what is meant by?validated evidence.........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(2)(c)???? The threshold frequency of lithium is 5.5 × 1014?Hz.(i)????? Calculate the work function of lithium, stating an appropriate unit,....................................................................................................................................................................................................................................................................................................................................................................................................................................................answer ...................................(3)(ii)???? Calculate the maximum kinetic energy of the emitted electrons when light of frequency 6.2 × 1014?HZ is incident on the surface of a sample of lithium...............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................answer ................................... J(3)(Total 12 marks)??Q27.????????? Electrons with a range of kinetic energies strike atoms of a particular element which are in their?ground state. As a result of these collisions photons of various frequencies are emitted by some of the atoms.(a)???? Explain what is meant by the ground state of an atom and describe the process that is taking place in the atoms emitting photons.The quality of your written communication will be assessed in this question.........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(6)(b)???? The table below shows how the kinetic energies of electrons with different incident energies may change after collisions with atoms.??kinetic energy of electron before collision/eVkinetic energy of electron after collision/eVFirst electron5.55.5Second electron9.01.0(i)????? Explain why one of the electrons loses energy while the other does not.....................................................................................................................................................................................................................................................................................................................................................................................................................................................(2)(ii)???? Convert the energy of 9.0 eV into joules....................................................................................................................................................................................................................................................................................................................................................................................................................................................(2)(iii)???? Calculate the?maximum?frequency of the photon emitted when the 9.0 ev electron collides with an atom...............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................answer ............................. Hz(3)(Total 13 marks)??Q28.????????? (a)?????Experiments based on the photoelectric effect support the particle nature of light. In such experiments light is directed at a metal surface.(i)??????State what is meant by the threshold frequency of the incident light...........................................................................................................................................................................................................................(1)(ii)?????Explain why the photoelectric effect is?not?observed below the threshold frequency.....................................................................................................................................................................................................................................................................................................................................................................................................................................................(2)(b)?????Monochromatic light of wavelength 5.40 × 10–7?m is incident on a metal surface which has a work function of 1.40 × 10–19?J.(i)??????Calculate the energy of a single photon of this light.?????answer = ...................................... J(2)(ii)?????Calculate the maximum kinetic energy of an electron emitted from the surface.???answer = ...................................... J(2)(iii)?????Calculate the maximum speed of the emitted electron.???answer = ...................................... m s–1(2)(iv)????Calculate the de Broglie wavelength of the fastest electrons.???answer = ...................................... m(2)(Total 11 marks)??Q29.????????? (a)?????A fluorescent tube is filled with mercury vapour at low pressure. In order to emit electromagnetic radiation the mercury atoms must first be?excited.(i)??????What is meant by an excited atom?..........................................................................................................................................................................................................................(1)(ii)?????Describe the process by which mercury atoms become excited in a fluorescent tube...............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(3)(iii)?????What is the purpose of the coating on the inside surface of the glass in a fluorescent tube?..............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(3)(b)?????The lowest energy levels of a mercury atom are shown in the diagram below. The diagram is?not?to scale.energy / J × 10–18?????????????????????????????????????????????????.................................................??? ? 0??????????????????????????????n?= 4??________________________??? –0.26???????????????????????????????????????n?= 3??________________________??? –0.59??????????????????????????????n?= 2??________________________??? –0.88????????????????? ground state?n?= 1??________________________??? –2.18(i)??????Calculate the frequency of an emitted photon due to the transition level?n?= 4 to leveln?= 3.????answer = ........................................ Hz(3)(ii)?????Draw an arrow on the diagram above?to show a transition which emits a photon of a longer wavelength than that emitted in the transition from level?n?= 4 to level?n?= 3.(2)(Total 12 marks)??Q30.????????? Electrons exhibit?wave properties.(a)?????What phenomenon can be used to demonstrate the wave properties of electrons? Details of any apparatus used are not required.............................................................................................................................................................................................................................................(1)(b)?????Calculate the de Broglie wavelength of electrons travelling at a speed of 4.50?×?105?m s–1.???answer = ..................................... m(2)(c)?????The muon has a mass equal to 207 times the mass of an electron.Calculate the speed of muons with the?same de Broglie wavelength as the electrons in part (b).????answer = ........................................ m s–1(3)(Total 6 marks)??Q31.????????? When a clean metal surface in a vacuum is irradiated with ultraviolet radiation of a certain frequency, electrons are emitted from the metal.??????????(a)???? (i)??????Explain why the kinetic energy of the emitted electrons has a maximum value.....................................................................................................................................................................................................................................................................................................................................................................................................................................................(2)(ii)?????Explain with reference to the work function why, if the frequency of the radiation is below a certain value, electrons are not emitted.....................................................................................................................................................................................................................................................................................................................................................................................................................................................(2)(iii)?????State a unit for work function..............................................................................................................(1)(b)?????Light energy is incident on each square millimetre of the surface at a rate of3.0 × 10–10?J s–1. The frequency of the light is 1.5 × 1015?Hz.(i)??????Calculate the energy of an incident photon.??answer = ....................................... J(2)(ii)?????Calculate the number of photons incident per second on each square millimetre of the metal surface.????answer = .........................................(2)(c)?????In the wave theory model of light, electrons on the surface of a metal absorb energy from a small area of the surface.(i)??????The light striking the surface delivers energy to this small area at a rate of3.0 × 10–22?J s–1.The minimum energy required to liberate the electron is 6.8 × 10–19?J.Calculate the minimum time it would take an electron to absorb this amount of energy.????answer = ....................................... s(1)(ii)?????In practice the time delay calculated in part c (i) does not occur. Explain how this experimental evidence was used to develop the particle model for the behaviour of light.....................................................................................................................................................................................................................................................................................................................................................................................................................................................(2)(Total 12 marks)??Q32.????????? (a)???? The photoelectric effect suggests that electromagnetic waves can exhibit particle-like behaviour. Explain what is meant by threshold frequency and why the existence of a threshold frequency supports the particle nature of electromagnetic waves.The quality of your written communication will be assessed in this question.............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(6)(b)???? (i)????? An alpha particle of mass 6.6 × 10–27?kg has a kinetic energy of 9.6 × 10–13?J.Show that the speed of the alpha particle is 1.7 × 107?m s–1.???(3)(ii)???? Calculate the momentum of the alpha particle, stating an appropriate unit.????answer = .....................................(3)(iii)???? Calculate the de Broglie wavelength of the alpha particle.???answer = ..................................... m(2)(Total 14 marks)??Q33.????????? Under certain circumstances, a photon moving through a material can interact with the nucleus of an atom of the material to produce an electron and a positron.(i)????? What is the name of this process?......................................................................................................................(1)(ii)????? Give one reason why the photon could not produce a single electron instead of an electron and a positron.........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(2)(iii)???? Make use of the Data and Formulae booklet to show that the minimum energy of the photon required for this process is 1.02 MeV.????(1)(iv)???? Photons whose wavelength exceeds a certain value will not cause this process.Calculate the maximum wavelength for the process to occur stating your answer to an appropriate number of significant figures.?????answer = ...................................... m(4)(v)???? Explain what will happen to the positron produced by the interaction.........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(2)(Total 10 marks)??Q34.????????? (a)?????Line spectra were observed before they could be explained by theory. We now know that photons of characteristic frequency are emitted when the vapour of an element is bombarded by energetic electrons. The spectrum of the light emitted contains lines,?each of a definite wavelength.Explain how???????? the bombarding electrons cause the atoms of the vapour to emit photons???????? the existence of a spectrum consisting of lines of a definite frequency supports the view that atoms have discrete energy levels.The quality of your written communication will be assessed in this question.............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(6)(b)?????The?ionisation energy?of a hydrogen atom is 13.6eV.(i)??????State what is meant by the ionisation energy of hydrogen...........................................................................................................................................................................................................................(2)(ii)?????Express the ionisation energy of hydrogen in joules, giving your answer to anappropriate number of significant figures.?????answer = ....................................... J(3)(Total 11 marks)??Q35.????????? (a)?????Line spectra were observed before they could be explained by theory. We now know that photons of characteristic frequency are emitted when the vapour of an element is bombarded by energetic electrons. The spectrum of the light emitted contains lines,?each of a definite wavelength.Explain how???????? the bombarding electrons cause the atoms of the vapour to emit photons???????? the existence of a spectrum consisting of lines of a definite frequency supports the view that atoms have discrete energy levels.The quality of your written communication will be assessed in this question.............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(6)(b)?????The?ionisation energy?of a hydrogen atom is 13.6eV.(i)??????State what is meant by the ionisation energy of hydrogen...........................................................................................................................................................................................................................(2)(ii)?????Express the ionisation energy of hydrogen in joules, giving your answer to anappropriate number of significant figures.?????answer = ....................................... J(3)(Total 11 marks)???M1.????????? (a)???? (i)????? the minimum energy?(1)energy required to eject a (photo)electron(from the metal surface)?(1)(ii)???? changing the metal/cathode?(1)3(b)???? conclusion:???? light below a?threshold frequency does notrelease electrons?(1)explanation:??? photons carry quanta of energy?(1)????????? [or conclusion: electrons are emitted immediately the??????????????????????? ? light hits the metal surface?(1)explanation:??? photons carry quanta of energy?(1)]2(c)???? (i)????? (use of?E = hf=??gives)?E?=??(1)4.14 × 10–19?(J)(ii)?????hf?=??+?Ek?(1)Ek?= 4.14 × 10–19?– 1.20 × 10–19?(1)???? = 2.94 × 10–19?(J)?(1)(allow C.E for value of?E?from (i))5[10]??M2.????????? (a)???? (i)????? electrons fall down from orbits or energy levels and emitlight/photons?(1)emitted wavelengths/frequencies/photon energies arediscrete?(1)[or the transitions are between definite/fixed (energy) levels?(1)(ii)???? C?→?B?(1)(iii)???? between D?→?C and C?→?A?(1)the two arrows must point down?(1)max 4(b)???? (i)????? (use of?hf?=?E2?–?El?gives)f?=??= 3.5 × 1014?Hz?(1)f?= 3.2 × 1014?(Hz)?(1)f?= 0.3 × 1014?(Hz)?(1)(ii)???? 4.6 × 10–19?(J)?(1)?= 2.9 (eV)?(1)5[9]??M3.????????? (a)???? electron diffraction or interference?(1)1(b)???? (use of?λ?=??gives)?λ?=??(1)= 1.46 × 10–9?m?(1)2(c)?????m??= 207 × 9.11 × 10–31?(kg)?(1)?( =?1.89 ×?10–28?(kg))(use of?meve?= mμvμ?, = when?λ?is constant, gives)vμ?=??(1)??? = 2.4 × 103?m s–1(2.41 × 103?m s–1)[or recalculate using?v?=?]3(d)???? gain in energy or work done on particle is the?same for both?(1)wavelength is inversely proportional to momentum?(1)gain in momentum is different for both?(1)the smallest mass has the largest acceleration/gain in speed?(1)[or wavelength proportional to?m–??with constant k.e.]max 2[8]??M4.????????? (a)???? (i)????? electrons behave as both particles and waves?(1)(ii)???? particle:? deflection in an electromagnetic field?????????????? or other suitable examples?(1)wave:???? electron diffraction?(1)3(b)???? (use of?λ?=?gives)?=?(1)= 4.28 × 106?m s–1?(1)2[5]??M5.????????? (a)???? (i)????? an electron moves?up?from one energy level to another??(1)(ii)???? an electron is removed from an atom? (1)2(b)???? (use of?hf?=?E2?–?E1?gives)????f?= (2.56 – 1.92) × 10–19??(1)/6.63 × 10–34= 9.65 × 1013?Hz(allow C.E. for incorrect?ΔE)2[4]??M6.????????? (a)???? the minimum frequency (of radiation)?(1)required to eject photoelectrons?(1)2(b)???? (i)????? (use of??=?hf0?gives)??= 6.63 × 10–34?× 4.85 × 1014??(1)= 3.22 × 10–19?(J)?(1)(ii)??????=?= 2.01 (eV)?(1)(allow C.E. for value of??from (i))3(c)???? line parallel to the given line with half the value of the?x- intercept2(d)???? statement : increase the light intensity/brightness??(1)????????? explanation : more incident photons (per second)?????????????????? one photon interacts with one electron???? (any two)? (1)? (1)?????????????????? more emitted electrons (per second)??????????????????? greater rate of?flow charge3QWC 2[10]??M7.????????? (a)???? there must be a large distance between collisions to allow?electrons to gain enough energy?(1)[or the vapour must not completely absorb the electrons]1(b)???? the mercury vapour emits ultra violet (radiation)?(1)the coating absorbs electromagnetic radiation/light fromthe mercury?(1)emits longer wavelengths/lower frequenciesin the visible region?(1)max 3QWC 2[4]??M8.????????? electrons diffract [or high energy electron scattering]?(1)showing wave behaviour?(1)electrons are deflected in electric or magnetic fields?(1)showing particle behaviour?(1)interference of electromagnetic waves?(1)showing wave behaviour?(1)photoelectric effect?(1)showing particle behaviour?(1)max 6QWC 2[6]??M9.????????? (a)???? (i)????? an electron/atom in an energy level/state or an orbiting electron?(1)is given energy?(1)to move to a higher level or orbit?(1)(ii)???? electromagnetic radiation is emitted when an electron falls?(1)from one fixed level to another fixed level?(1)giving the photon a discrete amount of energy?(1)max 5QWC 2(b)???? (i)????? (use of?E?=?hf?gives)?f?=??(1)?? ?(?=1.5 × 1015?(Hz))(use of?c?=?f?gives)????= 1.5??(1)= 2.0 × 10–7?m?(1)(ii)???? energy (in eV)??= 6.2 (eV)?(1)transition from n = 2 to n = 1?(1)(iii)???? line between n = 4 and n = 1?(1)direction from 4 to 1?(1)7[12]??M10.????????? (a)???? (use of?hf?=??+?Ek?gives) 3.2 × 10–19?=??+ 2.1 × 10–19?= 1.1 × 10–19??(1)?????? J?(1)3(b)???? incident energy of each photon is doubled6.4 × 10–19?= 1.1 × 10–19?+?EkEk?= 5.3 × 10–19?J?(1)3[6]??M11.????????? (a)???? (i)????? (use of?λ?=?gives)????v?=??(1)= 2.3 × 104?m s–1?(1)? ?(2.27 × 104?m s–1)(ii)???? (use of?λ?inversely proportional to?m?when?v?is constant, gives)?(1)=1.7 × 10–11?m?(1)[or??= 1.7 × 10–11?m (1.746 × 10–11?m)](allow C.E. for value of v from (a) (i)4(b)???? (i)????? diffraction (experiments)?(1)(ii)???? easier to obtain electrons (to accelerate)[or easier to get?λ?same size as scattering object]?(1)2QWC 2[6]??M12.????????? (a)???? electrons in energy levels/orbits?(1)excited to?higher?levels/orbits?(1)electrons relax/fall down and emit photons/em radiation?(1)photon energies/frequencies are discrete?(1)hence wavelengths are discrete?(1)intensity depends on number of photons per secmax 4(b)???? (ultraviolet) radiation (from mercury vapour) excites/absorbs?(1)the atoms of the powder in the tube?(1)these (atoms) de-excite and produce radiation?(1)radiation is visible light?(1)4[8]??M13.????????? (a)???? (Ek?=) maximum?(1)kinetic energy of the (emitted) (photo) electrons?(1)2(b)???? (i)????? (use of?f?=??gives)?f?=?= 1.6 × 1015?Hz?(1)?(1.58 × 1015?Hz)(ii)???? energy of incident photon (=?hf) = 6.6 × 10–34?× 1.6 × 1015or 1.1 × 10–18?(J)?(1)(allow C.E. for value of?f?from (i))(use of?f?= 1.58 × 1015?gives energy = 1.04 × 10–18?(J))incident energy is greater than the work function?(1)[or threshold frequency (=??) =?= 1.2 × 1015?(Hz)?(1)(incident) frequency is greater than the threshold frequency?(1)](iii)???? number of photons per sec is doubled(maximum) photon/electron (kinetic) energy is constantnumber (of photoelectrons) emitted (per second) is increased(or doubled)one photon collision with one electron????? (any three)?(1)?(1)?(1)6QWC 1[8]??M14.????????? (a)???? (i)????? k.e. =??(1)= 26 (eV)?(1)?(25.6 eV)(ii)???? (use of?λdB?=??gives)?λdB?=??(1)= 2.4 × 10–10?m?(1)?(2.42 × 10–10?m)4(b)???? (use of?hf?=?E1?–?E2?gives)?f?=??(1)(= 1.05 × 1015?(Hz))(use of?λ?=??gives)?λ?=??(1)= 2.9 × 10–7?m?(1)?(2.86 × 10–7?m)3[7]??M15.????????? (a)???? minimum (energy/work done)?(1)energy required to remove an electron fromthe surface (of the metal)?(1)2(b)???? (i)??????Ek?=?hf?–??(1)f0?= 0.50 × 1015?(Hz)?(1)?(=?hf0) = 6.6 × 10–34?× 0.50 × 1015?(1)= 3.3 × 10–19?J?(1)(ii)???? (use of?Ek?=?hf?–??gives)Ek?= (6.6 × 10–34?× 2.5 × 1015) – 3.3 × 10–19?(1)= 1.3(2) × 10–18?J?(1)(allow C.E. for incorrect value of??from (ii))[or (using gradient =?h?= ?Ek/?f)?Ek?= 6.6 × 10–34?× 2 × 1015?(1)= 1.3(2) × 10–18?J?(1)]6(c)???? same gradient?(1)drawn above existing line with smaller?x?intercept?(1)2[10]??M16.????????? (a)???? an electron is excited/promoted to a higher level/orbit?(1)reason for excitation: e.g. electron impact/light/energy externallyapplied?(1)electron relaxes/de-excited/falls back emitting a photon/em radiation?(1)wavelength depends on the energy change?(1)Max 3QWC 1(b)???? (i)????? use of?E?=?hf?gives)?E?=??(1)=??= 5.0 × 10–19?(J)?(1)(4.95 × 10–19?(J))and??= 9.9 × 10–19?(J)?(1)(ii)???? (energy of) level B = – 1.5 × 10–18?(J)?(1)level C = (–) 1.0 × 10–18?(J)?(1)5[8]??M17.????????? (a)???? (i)????? when an atom loses an orbiting electron (and becomes charged)?(1)(ii)?????(eV)?(1)?(257 (eV))2(b)???? (i)????? the electron in the ground state leaves the atom?(1)with remaining energy as kinetic energy (0.89 × 10?17?J)?(1)(ii)???? the orbiting electrons fall down?(1)to fill the vacancy in the lower levels?(1)various routes down are possible?(1)photons emitted?(1)taking away energy?(1)Max 4(c)???? E to D and D to B?(1)both in correct order?(1)2[8]??M18.????????? (i)??????(1)= 1.2 × 10?12?m?(1)?(1.17 × 10?12?m)(ii)??????(1)= 1.3?(1)?(1.28)(iii)???? (same de Broglie wavelength implies same momentum)mπνπ?=?m?ν??(1)?(1)(use of 1.3 gives 2.3(1)?× 106?ms?1)(allow C.E. from (ii))[6]??M19.????????? (a)???? work function?(1)minimum energy to remove an electron from the surface of a metal?(1)2(b)???? incident photon energy is fixed[or photoelectron receives a fixed amount of energy]?(1)photon loses all its energy in a single interaction?(1)electron can lose various amounts of energy to escape fromthe metal?(1)electrons have a maximum energy???photon energy ? workfunction?(1)Max 3(c)???? (i)??????φ?=?hf – Ek?(1)= 6.63 ×10?34?× 1.8 × 1015?? 4.2 × 10?19?(1)= 7.7(3) × 10?19?(J)?(1)(ii)?????(1)= 1.2 × 1015?Hz?(1)?(1.17 × 1015?Hz)(allow C.E. for value of?φ?from (i))5[10]??M20.????????? (a)???? (i)??????(3.40-1.51 = 1.89)ΔE=?1.89 × 1.60 × 10–19(J)?(1)(= 3.02 × 10–19(J))?(1)(=4.56 × 1014Hz)(ii)??????(1)(use of?f?= 4.6 × 1014?gives?λ?=?6.5 × 10–7m)3(b)???? (i)??????6 (wavelengths)?(1)(ii)???? (1.51–0.85) = 0.66(eV)?(1)2(c)?????mercury vapour at low pressure is conducting?(1)atoms of mercury are excited by electron impact?(1)producing (mainly) ultra violet radiation?(1)which is absorbed/ excites the coating?(1)which, upon relaxing, produces visible light?(1)electrons cascade down energy levels?(1)3[8]??M21.????????? (a)?????intensity determines the number of photons per second?(1)fewer photoelectrons per second?(1)(individual) photon energies are not changed?(1)with no change in the (kinetic) energy/speed?(1)one photon interacts with one electron?(1)3(b)?????energy of a photon is proportional to frequency (or?E = hf)?(1)photon of red light has less energy than a photon of blue light[orfred?<fblue?or?λred?>?λblue]?(1)the energy is insufficient to overcome the work function of the metal[or the frequency is below the threshold frequency]?(1)3(c)???? (i)??????Hz?(1)(ii)??????(1)=3.5 × 1014Hz??(1)(3.47 × 1014Hz)(iii)???? (use of??gives)Ex?= (6.63 x 10-34?x 1.5 x 1015) - 2.3 x 10-19?(1)7.6 × 10–19?(J)?(1)(7.645 × 10–19(J))(allow C.E for value of f from (i))5[11]??M22.????????? (a)???? The marking scheme for this part of the question includes anoverall assessment for the quality of written communication.There are no discrete marks for the assessment of writtencommunication but the quality of written communication willbe one of the criteria used to assign the answer to one of three levels.?LevelDescriptoran answer will be expected to meet most of the criteria in the level descriptorMark rangeGood?3–?? answer supported by appropriate range of relevant points–?? good use of information or ideas about physics, going beyond those given in the question–?? argument well structured with minimal repetition or irrelevant points–?? accurate and clear expression of ideas with only minor errors of spelling, punctuation and grammar6-7Modest?2–?? answer partially supported by relevant points–?? good use of information or ideas about physics given in the question but limited beyond this–?? the argument shows some attempt at structure–?? the ideas are expressed with reasonable clarity but with a few errors of spelling, punctuation and grammar3-5Limited?1–?? valid points but not clearly linked to an argument structure–?? limited use of information or ideas about physics1-20–?? unstructured–?? errors in spelling, punctuation and grammar or lack of fluency–?? incorrect, inappropriate or no response0physics points:???????? the energy of each photon/the light increases with frequency?(1)???????? electrons need a minimum amount of energy to leave the metal?(1)???????? the amount of energy required is equal to the work function?(1)???????? (this suggests) the electrons are given energy in one discrete eventor one electron interacts with one photon?(1)???????? (so the) light energy is not spread out it is concentrated (intoquanta)?(1)???????? the electron does not build up energy over time or photoelectricityoccurs immediately light falls on the metal?(1)(b)???? (i)??????E?=?hf?= 6.63 × 10–34?× 2.10 × 1015?= 1.39 × 10–18?(J)?(1)(ii)??????= hf?–?Ek?(1)= 1.39 × 10–18?– 6.20 × 10–19= 7.72 × 1019?J?(1)5[12]??M23.????????? (a)???? electrons can have wavelike properties and particle like properties?(1)1(b)???? (i)????? (use of λ =?h/mv)mv?= 6.63 × 10–34/1.2 × 10–10?(1)mv?= 5.5 × 10–24?(1)?kg m s–1?(1)?(or Ns)(ii)?????v?= 5.5 × 10–24/9.11 × 10–31?(1)v?= 6.1 × 106?m s–1?(1)(iii)???? (use of?E?= ?mv2)E?= ? × 9.11 × 10–31?× (6.1 × 106)2?(1)?(must see workingor equation)E?= 1.6(9) × 10–17?J?(1)?(no working max 1)7[8]??M24.????????? (a)?????QWCdescriptormark rangegood-excellentThe candidate provides a comprehensive and logical explanation which recognises that light consists of photons of energy?hf?and that an electron at or near the metal surface can only gain the energy of a single photon when it interacts with a photon. In addition, the candidate should recognise the significance of the work function (of the metal) in this context in relation to the maximum kinetic energy that an emitted electron can have. The candidate should also provide some indication of why the kinetic energy of an emitted electron may be less than the maximum kinetic energy. Although the term ‘work function’ might not be defined or used, the candidate’s explanation should clearly state that each electron needs a minimum amount of energy to escape from the metal.5-6modest-adequateThe candidate provides a logical and coherent explanation which includes the key ideas including recognition that light consists of photons of energy?hf?and that an electron at or near the metal surface can only gain the energy of a single photon when it interacts with a photon. In addition, the candidate should be aware that each electron needs a minimum amount of energy to escape from the metal. They should appreciate that the kinetic energy of an emitted electron is equal to the difference between the energy it gains from a photon and the energy it needs (or uses) to escape from the metal. However, the explanation may lack a key element such as why the kinetic energy of the emitted electrons varies.3-4poor-limitedThe candidate provides some correct ideas including recognition that light consists of photons of energy?hf?and that electrons in the metal (or at its surface) absorb photons and thereby gain energy. Their ideas lack coherence and they fail to recognise or use in their explanation the key idea that one photon is absorbed by one electron.1-2The explanations expected in a good answer should include most of the following physics ideasenergy is needed to remove an electron from the surfacework function?φ?(of the metal) is the minimum energy needed byan electron to escape from the surfacelight consists of photons , each of energy?E?=?hfone photon is absorbed by one electronan electron can escape (from the surface) if?hf?>?φkinetic energy of an emitted electron cannot be greater than?hf?–?φan electron below the surface needs to do work/uses energy to reachthe surfacekinetic energy of such an electron will be less than?hf?–?φ(b)???? (i)(ii)???? parallel line, higher threshold frequency?(1)(1)(iii)???? Planck’s constant?(1)4(c)???? (use of?hf0?=?)hf?= 6.63 × 10–34?× 2 × 5.6 × 1014?(1)?= 3.7(1) × 10–19?J?(1)Ek?= 2 × 3.7 × 10–19?– 3.7 × 10–19?= 3.7 × 10–19?J?(1)3[13]??M25.????????? (a)???? ionisation energy = 13.6eV?(1)1(b)???? (i)(ii)???? energy in Joules = 1.90?(1)?× 1.6 × 10–19?= 3.04 × 10–19?(J)?(1)(use of?E?=?hc/λ)3.04 × 10–19?= 6.63 × 10–34?× 3 × 108/λ?(1)(working/equation must be shown)λ = 6.54 × 10–7?m?(1)(1)?(2 or 3 sf for second mark)(accept 0.65 which gives an answer of λ = 1.91 × 10–6?m)8[9]??M26.????????? (a)???? (i)????? the (maximum) kinetic energy/speed/velocity/momentumof released electrons increases?(1)this is because increasing the frequency of the photons increasestheir energy?or?correct application of photoelectric equation?(1)(ii)???? the number of electrons emitted (per second) increases?(1)because there are now more photons striking the metal surface(per second)?(1)4(b)???? experiment/observation needs to be performed (to test a theory)?(1)the results of (the experiment) need to be proved/repeatable/replicated/confirmed?(1)[or?threshold frequency?(1)?could not be explained by the wavemodel?(1)]2(c)???? (i)????? (use of??=?hf0)?=?6.63 × 10–34?× 5.5 × 1014?(1)?=?3.65 × 10–19?(1)?J?(1)(ii)?????Ek?= 6.63 × 10–34?× 6.2 × 1014?(1)?– 3.65 × 10–19?(1)Ek?= 4.6 × 10–20?J (accept 5.1 × 10–20?J)?(1)6[12]??M27.????????? (a)???? the mark scheme for this part of the question includes an overallassessment for the Quality of Written Communication?QWCdescriptormark rangegood-excellentUses accurately appropriate grammar, spelling, punctuation and legibility.Uses the most appropriate form and style of writing to give an explanation or to present an argument in a well structured piece of extended writing.[May include formulae or equations].Answer refers to at least 5 of the relevant points listed below.5-6modest-adequateOnly a few errors.Some structure to answer, style acceptable, arguments or explanations partially supported by evidence or examples.Answer refers to at least 3 or the relevant points listed below.3-4poor-limitedSeveral significant errors.Answer lacking structure, arguments not supported by evidence and contains limited information.Answer refers to no more than 2 of the relevant points.1-2incorrect,inappropriateor noresponseNo answer at all or answer refers to unrelated, incorrect or inappropriate physics.0The explanation expected in a competent answer should include acoherent selection of the following physics ideas.electron in atoms can only occupy certain (discrete) energy levels?(1)the ground state is the lowest energy state an electron/atom can occupy?(1)electrons collide with (orbital) electrons?(1)giving the electrons the energy necessary to move to a higher level?(1)electrons later return to a lower level/ground state losing energy?(1)by emitting photons of a characteristic/different/discrete/certain/varying frequencies?or?ΔE?=?hf?or?frequency depends on energydifference?(1)(b)???? (i)????? the 5.5 eV electron does not have enough energy to excitean (orbital) electron/atom?(1)the 9.0 eV electron provide enough energy to excite an (orbital)electron/atom?(1)(ii)???? energy = 9.0 × 1.6 × 10–19?(1)?= 1.44 × 10–18?(J)?(1)(iii)?????E?= 1.44 × 10–18?– 1.6 × 10–19?= 1.28 × 10–18?(1)?(J)6.63 × 10–34?×?f?= 1.28 × 10–18?(1)f?= 1.28 × 10–18/6.63 × 10–34?= 1.9 × 1015?Hz?(1)7[13]??M28.????????? (a)???? (i)??????below a certain?frequency (called the threshold frequency)no electrons emitted?(1)or?minimum frequency for electrons to overcome work function1(ii)???? (light travels as photons) energy of a photon depends onfrequency?(1)below threshold frequency (photon) does not have enoughenergy?to liberate an electron?(1)or?reference to work function eg a photon does not have enoughenergy?(to allow the electron) to overcome the work function2(b)???? (i)????? (use of?E?=?hc/λ)E?= 6.63 × 10–34?× 3.00 × 108/5.40 × 10–7?(1)E?= 3.68 × 10–19?(J)?(1)2(ii)???? (use of?hf?=?Ek?+?)3.68 × 10–19?=?Ek?+ 1.40 × 10–19?(1)Ek?= 2.28 × 10–19?(J)?(1)2(iii)???? (use of?Ek?= mv2/2)2.28 × 10–19?= 1/2 × 9.11 × 10–31?×?v2?(1)v2?= 2 × 2.28 × 10–19/9.11 × 10–31?= 5.0 × 1011v?= 7.1 × 105?(m s–1)?(1)2(iv)??? (use of?λ?=?h/mv)λ?= 6.63 × 10–34(9.11 × 10–31?× 7.1 × 105)?(1)λ?= 1.03 × 10–9?(m)?(1)2[11]??M29.????????? (a)???? (i)????? an electron/atom is at a higher level than the ground state?(1)or?electron jumped/moved up to another/higher level1(ii)???? electrons (or electric current) flow through the tube?(1)and collide with orbiting/atomic electrons or mercury atoms?(1)raising the electrons to a higher level (in the mercury atoms)?(1)3(iii)???? photons emitted from mercury atoms are in the?ultraviolet?(spectrum)?or?high energy photons?(1)these photons are absorbed by the powder?or?powder changesfrequency/wavelength?(1)and the powder emits photons in the visible spectrum?(1)incident photons have a variety of different wavelengths?(1)max 3(b)???? (i)????? (use of?E?=?hf)–0.26 × 10–18?– 0.59 × 10–18?(1)?= 6.63 × 10–34?×?f?(1)f?= 0.33 × 10–18/(6.63 × 10–34) = 5.0 × 1014?(Hz)?(1)3(ii)?????one?arrow between n = 3 and n = 2?(1)?in correct direction?(1)2[12]??M30.????????? (a)???? (electron) diffraction/interference/superposition?(1)1(b)???? (use of?λ?=?h/mv)λ?= 6.63 × 10–34/(9.11 × 10–31?× 4.50 × 105)?(1)λ?= 1.6 × 10–9?(m)?(1)2(c)???? 207 × 9.11 × 10–31?(1)?×?v?= 6.63 × 10–34/1.6 × 10–7?(1)v?= 2200 (2170) (m s–1)?(1)3[6]??M31.????????? (a)???? (i)??????hf?is energy available/received?or?same energy from photons?(1)energy required to remove the electron varies (hence kineticenergy of electrons will vary)?(1)2(ii)???? (work function is the) minimum energy needed to releasean electron?(1)(or not enough energy to release electron)below a certain frequency energy of?photon?is less thanwork function?or?energy of?photon?correctly related to?f?(1)2(iii)???? joule?(1)?(accept eV)1(b)???? (i)????? (use of?E?=?hf)energy = 6.63 × 10–34?× 1.5 × 1015?(1)energy = 9.9 × 10–19?(J)?(1)2(ii)???? number of photons per second = 3.0 × 10–10/9.9 × 10–19?(1)number of photons per second = 3.0 × 108?(1)2(c)???? (i)????? (time taken = 6.8 × 10–19/3 × 10–22)time taken = 2.3 × 103?s?(1)1(ii)???? light travels as particles/ photons?(1)(or has a particle(like) nature)(which transfer) energy in discrete packets?(1)or?1 to 1 interactionor?theory rejected/modified (in light of validated evidence)2[12]??M32.????????? (a)?????The candidate’s writing should be legible and the spelling, punctuationand grammar should be sufficiently accurate for the meaning to beclear.The candidate’s answer will be assessed holistically. The answer will beassigned to one of the three levels according to the following criteria.High Level (good to excellent) 5 or 6 marksThe information conveyed by the answer is clearly organised, logical andcoherent, using appropriate specialist vocabulary correctly. The form andstyle of writing is appropriate to answer the question.The candidate provides a comprehensive and coherent description whichincludes a clear explanation of threshold frequency and why this cannot beexplained by the wave theory. The description should include a clearexplanation of the photon model of light and this should be linked to theobservations such as threshold frequency, the lack of time delay ormentions 1 to 1 interaction, the could not be explained by the wave model.Intermediate Level (modest to adequate) 3 or 4 marksThe information conveyed by the answer may be less well organised andnot fully coherent. There is less use of specialist vocabulary, or specialistvocabulary may be used incorrectly. The form and style of writing is lessappropriate.The candidate provides an explanation of threshold frequency and workfunction. The candidate explains the photon model of light and how this canprovide an explanation of threshold frequency, eg relates energy of photonto frequency or talks about packets of energy.Low Level (poor to limited) 1 or 2 marksThe information conveyed by the answer is poorly organised and may notbe relevant or coherent. There is little correct use of specialist vocabulary.The form and style of writing may only be partly appropriate.States what is meant by photoelectric effect. Knowledge of photons/packetsof energy.The explanation expected in a competent answer should include acoherent account of the significance of threshold frequency and howthis supports the particle nature of electromagnetic waves.?????????threshold frequency minimum frequency for emission of electrons?????????if frequency below the threshold frequency, no emissioneven if intensity increased?????????because the energy of the photon is less than the work function?????????wave theory can not explain this as energy of waveincreases with intensity?????????light travels as photons?????????photons have energy that depends on frequency?????????if frequency is above threshold photon have enough energy?????????mention of lack of time delaymax 6(b)???? (i)????? use of?Ek?=?? × 6.6 × 10–27?(1)?×?v2?= 9.6 × 10–13?(1)v2?= 2.91 × 10–14?(or?v?=?√2.91 × 10–14)?(1)(v?= 1.7 × 107?m s–1)3(ii)???? (use of?p?=?mv)p?= 6.6 × 10–27?× 1.7 × 107?(1)p?= 1.1 × 10–19?(1)?kg m s–1/N s?(1)3(iii)???? (use of?λ?=?)λ?= 6.63 × 10–34/1.1 × 10–19?(1)λ?= 5.9 × 10–15?m?(1)?(6.03 × 10–15?m)2[14]??M33.????????? (i)????? pair production?(1)1(ii)????? conservation law stated (charge or lepton number)?(1)shown to be true eg lepton number +1–1 = 0?(1)2(iii)???? energy = 2 × 0.510 (ignore sfs)?(1)1(iv)???? E = (1.02 × 1.6 × 10–13) = 1.63 × 10–13?(1)1.63 × 10–3?= 6.63 × 10–34?× 3.00 × 108/λ?(1)λ?= 6.63 × 10–34?× 3.00 × 108/1.63 × 10–13?= 1.22 × 10–12?m?(1)3 significant figures?(1)4(v)???? will encounter an?electron?and the two particles will annihilate?(1)releasing (two high energy/gamma)?photons/quanta?(1)2[10]??M34.????????? (a)?????The candidate’s writing should be legible and the spelling,punctuation?and grammar should be sufficiently accuratefor the meaning to be clear.The candidate’s answer will be assessed holistically. Theanswer will be?assigned to one of three levels according to thefollowing criteria.High Level (Good to excellent): 5 or 6 marksThe information conveyed by the answer is clearly organised,logical and coherent, using appropriate specialist vocabularycorrectly. The form and?style of writing is appropriate to answerthe question.The candidate provides a comprehensive and coherentdescription which includes a clear explanation of constantenergy level differences and how electrons can be excitedby electron collisions. The link between the energy of a photonand its frequency should be clear. The description shouldinclude a clear explanation of the reason atoms of a givenelement emit photons of a characteristic frequency?or?thereis a clear link between constant energy differences and photonfrequency/wavelength (eg E=hf).The candidate should relate the energy?difference?betweenlevels to the energy of emitted photons and state the energydifference is fixed/constant.Intermediate Level (Modest to adequate): 3 or 4 marksThe information conveyed by the answer may be less wellorganised and not fully coherent. There is less use of specialistvocabulary, or specialist vocabulary may be used incorrectly.The form and style of writing is less appropriate.The candidate provides an explanation of energy levels andhow excitation takes place by electron collision with?atomic/orbital?electrons. The candidate explains how anorbital/atomic electron loses energy by emitting a?photon.Low Level (Poor to limited): 1 or 2 marksThe information conveyed by the answer is poorly organisedand may not be relevant or coherent. There is little correctuse of specialist vocabulary.The form and style of writing may be only partly appropriate.Some mention of energy levels and the idea of excitation ofelectron. Talk?about excitation of atom instead of electron limitsthe mark to 1.Incorrect, inappropriate of no response: 0 marksNo answer or answer refers to unrelated, incorrect or inappropriate physics.The explanation expected in a competent answer should include acoherent account of the significance of discrete energy levelsand how?the bombardment of atoms by electrons can lead toexcitation and the subsequent emission of photons of a characteristicfrequency.electrons bombard atoms of vapour and give energy to electrons in atomelectrons move to a higher energy levelelectrons are excitedexcited electrons move down to lower energy levels losing energy byemitting photonsphotons have energy hfphotons of characteristic frequencies emitted from atoms of aparticular?elementthis is because atoms have discrete energy levels which areassociated with particular energy valuesmax 6(b)???? (i)????? energy required to (completely) remove an electronfrom atom/hydrogen?ground state/lowest energy level?2(ii)???? 13.6 × 1.6 × 10–19??= 2.18 × 10–18?(J)??3 sfs?3[11]??M35.????????? (a)?????The candidate’s writing should be legible and the spelling,punctuation?and grammar should be sufficiently accuratefor the meaning to be clear.The candidate’s answer will be assessed holistically. Theanswer will be?assigned to one of three levels according to thefollowing criteria.High Level (Good to excellent): 5 or 6 marksThe information conveyed by the answer is clearly organised,logical and coherent, using appropriate specialist vocabularycorrectly. The form and?style of writing is appropriate to answerthe question.The candidate provides a comprehensive and coherentdescription which includes a clear explanation of constantenergy level differences and how electrons can be excitedby electron collisions. The link between the energy of a photonand its frequency should be clear. The description shouldinclude a clear explanation of the reason atoms of a givenelement emit photons of a characteristic frequency?or?thereis a clear link between constant energy differences and photonfrequency/wavelength (eg E=hf).The candidate should relate the energy?difference?betweenlevels to the energy of emitted photons and state the energydifference is fixed/constant.Intermediate Level (Modest to adequate): 3 or 4 marksThe information conveyed by the answer may be less wellorganised and not fully coherent. There is less use of specialistvocabulary, or specialist vocabulary may be used incorrectly.The form and style of writing is less appropriate.The candidate provides an explanation of energy levels andhow excitation takes place by electron collision with?atomic/orbital?electrons. The candidate explains how anorbital/atomic electron loses energy by emitting a?photon.Low Level (Poor to limited): 1 or 2 marksThe information conveyed by the answer is poorly organisedand may not be relevant or coherent. There is little correctuse of specialist vocabulary.The form and style of writing may be only partly appropriate.Some mention of energy levels and the idea of excitation ofelectron. Talk?about excitation of atom instead of electron limitsthe mark to 1.Incorrect, inappropriate of no response: 0 marksNo answer or answer refers to unrelated, incorrect or inappropriate physics.The explanation expected in a competent answer should include acoherent account of the significance of discrete energy levelsand how?the bombardment of atoms by electrons can lead toexcitation and the subsequent emission of photons of a characteristicfrequency.electrons bombard atoms of vapour and give energy to electrons in atomelectrons move to a higher energy levelelectrons are excitedexcited electrons move down to lower energy levels losing energy byemitting photonsphotons have energy hfphotons of characteristic frequencies emitted from atoms of aparticular?elementthis is because atoms have discrete energy levels which areassociated with particular energy valuesmax 6(b)???? (i)????? energy required to (completely) remove an electronfrom atom/hydrogen?ground state/lowest energy level?2(ii)???? 13.6 × 1.6 × 10–19??= 2.18 × 10–18?(J)??3 sfs?3[11]???E1.????????? Many candidates are still not clear of the meaning of the term ‘work function’ and a large number referred to an electron being ionised or escaping from an atom. Candidates also implied that removing an electron occurred at a specific photon energy rather than at or above a specific photon energy. Only the better candidates realised that changing the metal would change the work function.In (b) several candidates chose to describe an aspect of the photoelectric effect that could be explained in terms of a wave phenomenon rather than particle phenomenon and missed one of the two marks available. The idea that photons carry quanta of energy was widely appreciated.The calculation in part (c) was performed well by a majority of candidates but for the others it was deciding the frequency to use in the photoelectric equation that caused most problems.?E2.????????? Many candidates in part (a) did not make it clear that photons are emitted when electrons drop down an energy level. It was common for candidates to describe the process of excitation in detail, a description which was not required in the question. This confusion persisted into part (a)(iii) were the two arrows were often shown pointing upwards.A typical script showed a correct calculation in (b)(i) but only the very best candidates gave the three frequencies. A large number of candidates showed errors in powers of ten because the factor 10–19, shown in the energy diagram, was not used. In part (b)(ii) a large number of candidates failed to convert J to eV because they multiplied rather than divided by 1.6 × 10–19, thus giving ridiculous answers.?E3.????????? Most candidates knew that electrons exhibited wave properties when they were diffracted but it was sad to see that the correct spelling of diffraction was accomplished by only a minority of candidates. The de Broglie calculation in part (b) was attempted correctly by most candidates but a significant number gave an answer to only 1 significant figure. This showed that candidates did not set their calculator to display scientific notation and 0.000000001 was unthinkingly used as the final answer.Part (c) was found to be a little more difficult than part (b) due to the given information being fairly complicated and also the need to rearrange the working equation.Part (d) proved to be difficult even for the good candidate. Many candidates made links between variables without any justification; for example, “the wavelength must be different because their masses are different”, appeared frequently. Also, vague statements rather than specific statements were made, e.g. candidates stated that the mass of the moon was different rather than larger than that of the electron.?E4.????????? Most candidates were aware of wave particle duality, but they sometimes lost marks through lack of care. For example, a statement such as “an electron can behave as a wave or as a photon” was common but did not gain any marks. In identifying the behaviour of electrons, weaker candidates often gave an example but failed to state which type of behaviour it represented.In part (b) only the weaker candidates had trouble with the calculation. They either failed to use the de Broglie equation or could not rearrange the equation to make the speed,?v, the subject.?E5.????????? The topics in part (a), namely excitation and ionisation, have been examined before and, as on previous occasions, candidates tried to explain the full excitation and relaxation processes instead of simply stating that an electron is promoted up to a different energy level in the excitation process. Ionisation was understood much better, but too many students thought the incoming electron was captured by the atom. Although it is appreciated that temporary negative ions or resonances occur for extremely short time periods no marks were awarded for electron capture because it would be outside the experience of candidates.The most common error in part (b) was not identifying the correct change in energy. Also, the 10–19?factor in the given energies was omitted in many of the calculations.?E6.????????? Although, in general, the majority of answers were satisfactory a considerable number of candidates had trouble in part (a) when attempting to explain the meaning of the term?threshold frequency. Very often they could not distinguish between work function and threshold frequency.The calculations in part (b) were carried out very well, especially when determining the value of the work function in Joules, but only the better candidates could convert Joules to eV.Part (c) was also tackled well and only the weaker candidates failed to draw the additional line on the graph.Part (d) gave candidates the opportunity to air their knowledge of the photoelectric effect but there are still many candidates who do not appreciate the difference between changing the intensity and changing the frequency of the incident electromagnetic radiation. However, the written accounts indicated that more candidates this year than in previous years understood this point.?E7.????????? Answers to this short question showed that most candidates had no real idea of how a fluorescent light tube worked and many accounts were pure guesswork. Some of the most common errors were, stating, in part (a), that the tube was under low pressure so that it would not break and in part (b), believing that the electrons were directed at the coating in order to make it glow.?E8.????????? Too much time was spent by candidates repeating the wording of the question and explaining the wave particle duality. There was also a tendency to concentrate on one or two pieces of evidence, thereby excluding themselves from gaining full marks because of the lack of coverage. It was this aspect of the submitted answers that really governed the marks awarded, rather than candidates making errors. It was also clear that many candidates thought it only necessary to discuss the wave view of an electron and the particle view of an electromagnetic wave.?E9.????????? The explanation of the excitation process in part (a)(i) was done well. There were very few references to ionisation, which has occurred in previous papers, and also practically no candidates referred to an electron leaving a metal. There was a tendency to continue the explanation into the relaxation process, which was unnecessary. In part (ii) several candidates worked backwards to the expected answer. These candidates typically wrote that the wavelength was fixed because the frequency was fixed because the energy was fixed. It was easy for these candidates to miss the relevant marking points. Very few candidates gave clear statements about the energy levels occurring at discrete energies or that an electron drops down an energy level when a photon was emitted.Part (b) again proved to be a good discriminator. In part (i) several candidates attempted to use the de Broglie relationship instead of the usual?λ?=?ch/E. In parts (ii) and (iii) only about half the candidates gave the correct transition and the correct direction. Most of them successfully converted the energy of the transition from joules into eV.?E10.????????? Part (a) caused problems for a significant number of candidates. It was common to find the frequency of the incident radiation being calculated and then the value substituted back into the photoelectric equation in order to calculate the energy. The unit of work function was often incorrect, resulting in a lost mark.Part (b) discriminated very well, even in the top ability range. For those candidates who failed on this part, some of the more common errors were: taking the energy to be proportional to the wavelength, doubling the value of the work function instead of doubling the incident energy of each photon and basing the energy of the photon on the photoelectron energy.?E11.????????? Part (a) proved to be a good discriminator. Although it was a basic question on the de Broglie wavelength, the weaker candidates lost marks on significant figures, units, using the wrong mass and making arithmetic errors.Part (b) also discriminated against those who did not think carefully about their answers. Some referred to the Young fringes, which mainly relates to optical interference. Also, statements such as ‘electrons are easier to see’ showed lack of thought.?E12.????????? The average candidate scored well in part (a), where there were six available marking points, but frequently missed out by stating that photon energies or frequencies were discrete and consequently so were the wavelengths of electromagnetic radiation.Again, the average and good candidates found part (b), on the fluorescent tube, straightforward. Others however, wanted to refer to the photoelectric effect in some way or discuss the false idea that electrons in the tube collided with the coating on the wall of the tube. However, the number of candidates being side-tracked in this way were far fewer than on similar questions in previous papers. The availability of previous papers has made significant improvements to the quality of answers submitted on the topic of the fluorescent tube.?E13.????????? Less able candidates gave the answer to part (a) as simply as ‘kinetic energy’. They obviously had not responded to the two available marks. Apart from this it was quite common to see only one mark being awarded because candidates would omit referring to it as the maximum kinetic energy or as the kinetic energy of the emitted electrons. Some candidates even referred to ‘energy needed’, which showed a misunderstanding of the given equation.Parts (b) (i) and (ii) proved difficult for the weaker candidates. Several tried to use the photoelectric equation to determine the frequency and consequently became very confused. The majority of candidates, however, knew how to tackle this question and showed that the kinetic energy of the electron was positive. A minority of candidates took the alternative approach and showed the incident frequency was greater than the threshold frequency. The explanation required in part (b) (iii) used to be the type of question that produced wrong answers from the majority of candidates, because very often they could not distinguish between the role of the incident electromagnetic frequency and the role of the incident intensity. It is pleasing to report that in this examination it was only the weaker candidates who showed this uncertainty. This was one of the reasons for assuming that the present cohort of candidates were slightly better than average.?E14.????????? Parts (a) and (b) of this question showed errors at different levels of ability. The slightly better candidates used the correct equations but often used the speed of light in the de Broglierelationship. The very weak candidates did not know when to apply??or. In other cases, the wrong energy was used to calculate the wavelength of aphoton and it was not uncommon to see the electron energies at levels D and B being added together.Part (a) (i) in particular showed a variety of errors. Multiplying, rather than dividing by the electron charge was the obvious error. Some of the better candidates used the electron speed to calculate the kinetic energy, arriving at the energy in joules which had already been given in the question, and then failing to convert this to eV. About 15% of the candidates incurred a significant figure error on this question by quoting an answer to five significant figures.??E15.????????? In defining?work?function?in part (a), most candidates wrote about the energy required to eject an electron from a metal, rather than referring to a minimum energy requirement.More than 50% of the candidates tackled part (b) in a sensible way and chose the correct frequency to use in each part. There was, however, plenty of scope for errors in powers of 10, significant figures and units. Many candidates failed to realise that the threshold frequency was 0.5 × 1015?Hz from the graph. There were also a significant number of candidates who could not attempt these calculations. In part (c), about 50% of the candidates drew the graph with confidence, while the remainder simply made a guess.?E16.????????? The description of how an excitation spectrum was produced was generally done well in part (a), but many candidates omitted the fact that energy had to be provided by some means to start the process.In part (b) (i), candidates who were aware of the equation?E?=?hc/λ?completed the calculations correctly, but there were a few significant figure errors and several candidates had trouble with powers of 10. The determination of the energy levels B and C in part (b) (ii) caused considerable difficulty, with only a minority of candidates obtaining the correct answers. The connection between the photon energies and the energy levels was not obvious to most candidates.?E17.????????? Part (a), on the whole, was answered quite well. The common error which occurred in part (a) (ii) was to multiply rather than divide by the electron charge.In part (b), the more able candidates considered the electron emitted from the atom in an ionisation process, the electron taking with it the remaining energy as kinetic energy. Most candidates did discuss ionisation and obtained a mark, but many thought an electron was only promoted up a few energy levels.In part (b) (ii), only the most able candidates considered electrons in higher orbits cascading down energy levels, emitting photons as they eventually occupied the ground state.The incorrect answer of D → C and C → B in part (c) was very common, probably because the gaps between the lines in the diagram looked approximately the same.?E18.????????? This question discriminated very well, again because of the errors incurred. In addition to getting the basic physics wrong, all the following errors were seen; using the wrong numerical data when substituting for symbols, incorrectly rearranging the equations, calculation errors, failing to give the correct units and giving the answer to the wrong number of significant figures.Some of the more able candidates made more work for themselves in part (ii), by trying to convert the numerator and denominator to Kg, rather than cancelling out the units at an early stage in the calculation. On the positive side, nearly all the candidates had very little difficulty in finding the necessary information about the particles from the?Rest Energy?column in the Data Sheet.?E19.????????? Part (a), in general, performed well, even though the question asked for the definition of the work function in an indirect way. In the early years of the current specification, candidates often interchanged ideas about photoelectric emission with ionisation. In latter years candidates have been much better at distinguishing between these two phenomena, but unfortunately these misconceptions returned in part (b) this year.Previous questions have focused mainly on the distinction between the energy and intensity of the incident light. The current question asked about the range of kinetic energy of the photoelectrons, which was a new approach. In their search for an answer, the majority of candidates either thought that the electrons must be in the excited states of the metal atoms or that they absorbed only a fraction of the photon energy.Although part (c) was a straightforward calculation, it did discriminate, simply because of the errors generated.?E20.??????????Part (a) was answered well. Some candidates worked backwards from the frequency value and failed to score full marks, not because of the order of the calculations but because they did not include the stage of changing eV into Joules. It was also quite common to omit units for the wavelength. There were very few correct answers to part (b) (i). Answers to part (b) (ii) were better, but a number of good candidates misread the question and tried to determine the wavelength.Only the more able candidates scored well in part (c), even though there were six marking points for the three available marks. All the misconceptions, e.g. the electrons hitting the coating, could be listed, but in truth most candidates did not know what happened in a fluorescent tube and wrote about anything that came to mind. A general feature of many answers was that candidates too readily combined more than one idea in a single sentence, thereby making their ideas unclear. It would be of benefit to most candidates to give simple clear statements, one sentence to each idea or process, and for these to run in a chronological order.?E21.??????????Part (a) was answered very poorly. Most candidates realised that there were fewer photoelectrons but this was rarely quoted as a rate and the reasons given were often suspect. It was a commonly held view that the change in intensity changed the energy.Part (b) produced better marks. The change in the frequency or wavelength was known to most candidates and about 50% of them referred to the work function or threshold frequency. Less able candidates just wrote about the wavelength being different, which was not acceptable. Overall, candidates did not seem to be as knowledgeable in distinguishing between the effects of intensity and frequency of the source as in previous examinations. Part (c) caused a few problems for less able candidates because they were often confused between?f0?and/?E23.????????? Part (a) was answered reasonably well and candidates generally understood the meaning of particle wave duality. Some candidates just referred to wave properties, presumably assuming that particle properties were self-evident.In part (b) (i) it was noticeable that less able candidates confused momentum with energy. The unit for momentum also caused significant problems. The penalty for not being able to calculate momentum was not a major one, as consequential error was allowed for parts b (ii) and b (iii).?E24.????????? Part (a) was not answered well and there was much confusion as to the processes involved in the photoelectric effect. However, a significant number of candidates confused the effect with excitation and line spectra. Only a minority of candidates were able to explain why the kinetic energy of the emitted electrons varied. A common response referred to the photons having a variety of energies even though the question stated that the light had a certain frequency. Most answers lacked significant detail such as the idea that a photon interacts with one electron and how threshold frequency and work function are related.This question assessed quality of written communication and it was clear that most candidates appreciated that their answers needed a logical structure. However, few candidates were able to give a coherent and comprehensive answer.Part (b) generated better answers although a significant minority of candidates did not appreciate the fact that the gradient of the maximum kinetic energy against frequency graph is the Planck constant.Part (c) proved more difficult than expected and a number of candidates calculated the energy of the photon using the threshold frequency and failed to calculate the work function.?E25.????????? Correct responses for part (a) were common, although a significant minority of candidates did give the answer 12.75 eV which is the energy change from level one to level four.The other parts of the question were answered well by the majority of candidates, with the only common errors occurring in the transition diagram, where often too many arrows were drawn or the arrows were shown in the wrong direction or there was no arrow at all. The calculation in part (b) (ii) was approached with confidence by many candidates and most appreciated that they were required to limit the number of significant figures in their answers.?E26.????????? Part (a) was answered reasonably well and candidates seemed to appreciate the effects of changing the frequency and changing the intensity of the incident light. In the legacy specification, this topic has often confused candidates and it was pleasing to see many confident responses. A minority of less able candidates did confuse the meaning of frequency, taking it to mean the rate of photon arrival rather than the frequency of individual photons.Part (b) (iv) assessed How Science Works and candidates answered this question well, demonstrating that the idea of validated evidence is well understood.The calculation in part (c) was, for the most part, done well and identifying the unit for the work function did not really cause many problems. The only common error occurred in part (c) (ii) when the maximum kinetic energy was calculated by equating it to the photon energy and ignoring the work function in spite of the fact that this had been successfully calculated in part (c) (i).?E27.????????? Candidates usually find questions involving a description of the formation of line spectra difficult. This proved to be the case this time and many candidates were very confused in their answers to part (a). A common error was to mix up this effect with the photoelectric effect even though the question mentioned the emission of photons. Many less able candidates talked about photons being absorbed rather than electron collisions and the idea of discrete energy levels and their relationship to the frequency of characteristic photons did not seem well understood. This question assessed the Quality of Written Communication and candidates tended to fail to gain marks because there was not a logical structure in the physics used in their explanations.Part (b) (i) was not done well and many candidates confused the incident electrons with the orbital electrons and made statements such as ‘one of the electrons is excited and loses energy while the other one is in its ground state’. Candidates in the main, did not link this with part (a).Part (b) (i) and (ii) proved to be much more accessible and full marks were common. The only common error was to use 9.0 eV instead of 8.0 eV as the energy of the photon.?E28.????????? Part (a) was not answered well and there was much confusion as to the processes involved in the photoelectric effect. As has been the case in the past, a significant number of candidates confused the effect with excitation and ionisation of atoms. Only a minority of candidates were able to link the energy of a photon to its frequency and there was much confusion between threshold frequency and the work function. It was not unusual to see responses that stated the threshold frequency has to equal the work function. It also seems that some candidates are under the impression that the photoelectric effect involves the emission of photons – presumably due to confusion between excitation and line spectra.Part (b) proved to be a familiar calculation for the majority of candidates and many competent answers were seen. The only significant misunderstanding occurred in (b) (iii) when candidates assumed that the kinetic energy of the electron is found by using the equation for the energy of a photon.?E29.????????? Part (a) proved to be quite discriminating and less able candidates found it hard to explain the process by which mercury atoms become excited in a fluorescent tube. There was also evidence to suggest that some candidates think that excitation only occurs due to the absorption of photons and seemed unaware that it can also happen by electron collision. Most candidates seemed to appreciate that the mercury atoms emitted photons that were in the ultraviolet part of the spectrum and that the coating changed the frequency of these although there was a tendency to describe these photons as photons of light or coloured light rather than visible light.Part (b) was answered well and the only common error was a failure to appreciate that the energy levels were in Joules and that the value adjacent to each level needed to be multiplied by 10–18. A minority of candidates either emitted this factor or assumed that the energies were in electron volts and multiplied them by 1.6 × 10–19.?E30.????????? This question was well answered and the majority of candidates appreciated that diffraction is a wavelike property that electrons exhibit. The calculation in part (b) proved to be quite straightforward and full marks were obtained by a pleasing number of candidates.?E31.????????? The initial parts of this question caused considerable problems to candidates. They found it very difficult to explain why the kinetic energy of the emitted electrons had a maximum value and also fully explain the link between photon energy, work function and maximum kinetic energy. The idea that some electrons require more energy to be emitted than others did appear to be well understood. Candidates also had a tendency to confuse the photoelectric effect with excitation and ionisation. Evidence from this and previous papers suggests that this is a topic candidates find very difficult and this is particularly true when they are required to explain aspects of the phenomena.Parts (b) and (c) proved much more accessible and candidates used the various relevant equations confidently. Full marks for calculations were quite common. Part (c) (ii), which assessed?How Science Works, did confuse some candidates. When this happened, candidates tended to explain the significance of validated evidence in general terms, rather than how it was used to develop the particle model of light.?E32.????????? Descriptive questions on the photoelectric effect have in the past caused candidates major problems, it was therefore good to see so many confident answers this series. There was strong evidence that the concept of threshold frequency is now understood much better. Many candidates correctly explained the term and also were able to give a detailed explanation of its significance in the particle model of light. The one to one interaction and lack of time delay in the emission of electrons was also explained well in a high proportion of answers. Some good responses were not fully developed however, as they did not contrast the behaviour of photons with the behaviour of waves. This question also assessed the quality of written communication and most answers were well structured and expressed with clarity and precision.The calculations in part (b) were answered well, although some less able candidates were unable to correctly use the equation for kinetic energy. There was a dedicated mark for the unit of momentum in part (ii) and, as is often the case, candidates found this a difficult unit to recall.?E33.????????? This question on pair production suggested that while candidates are for most part, familiar with the process they do have the tendency to become confused when more details are required. The majority correctly identified the process and were able to use lepton or charge conservation effectively to explain why a positron must be produced along with the electron. They did however, find the quantitative aspect more of a challenge and it was not uncommon to see overcomplicated answers or no attempt made to answer part (iii).The calculation for maximum wavelength in part (iv) was answered well by the more able candidates but others found this difficult. Common errors were not converting rest mass energy to joules and the use of energy as momentum when the equation for the de Broglie wavelength was used in error. Good answers to part (v) were frequently seen, although some candidates are under the impression that the positron annihilates with the electron produced rather than another electron.?E34.????????? Descriptive questions on quantum phenomena have caused candidates major problems in previous papers. Therefore, it was good to see so many confident answers to this question. Candidates seemed much more confident explaining excitation and line spectra than they are describing aspects of the photoelectric effect. Far less confusion was evident and a number of answers were awarded marks in the top band – a significant increase on previous questions that assessed the quality of written communication. Some less able candidates incorrectly tried to include a discussion of threshold frequency but this was comparatively rare. The correct use of technical terms such as ionisation and excitation were seen frequently and there was strong evidence that this aspect of quantum phenomena is more widely understood that is the case in other related areas of the specification.Part (b) was generally answered well, although a minority of candidates incorrectly related the ionisation energy of hydrogen to a mole of hydrogen atoms. The conversion of electron volts to joules caused few problems and the majority of candidates appreciated that their answer should be quoted to three significant figures.?E35.????????? Descriptive questions on quantum phenomena have caused candidates major problems in previous papers. Therefore, it was good to see so many confident answers to this question. Candidates seemed much more confident explaining excitation and line spectra than they are describing aspects of the photoelectric effect. Far less confusion was evident and a number of answers were awarded marks in the top band – a significant increase on previous questions that assessed the quality of written communication. Some less able candidates incorrectly tried to include a discussion of threshold frequency but this was comparatively rare. The correct use of technical terms such as ionisation and excitation were seen frequently and there was strong evidence that this aspect of quantum phenomena is more widely understood that is the case in other related areas of the specification.Part (b) was generally answered well, although a minority of candidates incorrectly related the ionisation energy of hydrogen to a mole of hydrogen atoms. The conversion of electron volts to joules caused few problems and the majority of candidates appreciated that their answer should be quoted to three significant figures.?? ................
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