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UNIT : 7 - DUAL NATURE OF RADIATION AND MATTER ONE MARK QUESTIONS:An electron and alpha particle have the same de-Broglie wavelength associated with them. How are their kinetic energies related to each other?The stopping potential in an experiment on photoelectric effect is 2 V. What is the maximum kinetic energy of the photoelectrons emitted?Show graphically, the variation of the de-Broglie wavelength (λ) with the potential (V) through which an electron is accelerated from rest.The graph shows variation of stopping potential V0 versus frequency of incident radiation ν for two photosensitive metals A and B. Which of the two metals has higher threshold frequency and why?190500351790 Name the phenomenon which shows the quantum nature of electromagnetic radiation.Which experiment establishes the wave nature of the particle?Which optical phenomenon is exhibited by the particle in famous Davisson – Germer Experiment?ANSWER OF ONE MARK QUESTIONS:We have λ= h/√2mk or k=h2/2m λ 2 . as λ e = λa me< ma so ke > kaThe maximum kinetic energy of the photoelectrons emitted = 1.6×10-19 ? 2V = 3.2× 10-19JMetal A , because ?0 ′ > ?0Photoelectric effect shows the quantum nature of electromagnetic radiation.The wave nature of the particle is established by Davisson- Germer Experiment.Diffraction of light.TWO MARKS QUESTIONS:In a photoelectric effect experiment, the following graphs were obtained between the photoelectric current and the applied voltage. Name the characteristics of the incident radiation (a) that was kept constant (b) that was variable in this experiment139065050800A proton and an -particle are accelerated through the same potential difference. Which one of the two has (i) greater de-Broglie wavelength, and (ii) less kinetic energy? Justify your answer.ANSWER OF TWO MARKS QUESTIONS: (a)Frequency of radiation (b) Intensity of radiation35242554610THREE MARKS QUESTIONSAn electromagnetic wave of wavelength λ is incident on a photosensitive surface of negligible work function. If the photo-electrons emitted from this surface have the de-Broglie wavelength λ 1 , prove that λ =(2mc/h) λ21.Plot a graph showing the variation of stopping potential with the frequency of incident radiation for two different photosensitive materials having work functions w1 and w2 (w1 > w2). What is the significance of (i) slope and (ii) intercept of the lines depend?(a) Why photoelectric effect cannot be explained on the basis of wave nature of light? Give reasons. (b) Write the basic features of photon picture of electromagnetic radiation on which Einstein’s photoelectric equation is based. The given graph shows the variation of photo-electric current (I) versus applied voltage (V) for two different photosensitive materials and for two different intensities of the incident radiation. Identify the pairs of curves that correspond to different materials but same intensity of incident radiation.1390650247015 Light of intensity ‘I’ and frequency ‘’ is incident on a photosensitive surface and causes photoelectric emission. What will be the effect on photo current whenthe intensity of light is gradually increased, the frequency of incident radiation is increased, and the anode potential is increased?In each case, all other factors remain the same. Explain, giving justification in each case.State two important properties of photon which are used to write Einstein’s photoelectric equation. Define (i) stopping potential and (ii) threshold frequency, using Einstein’s equation and drawing necessary plot between relevant quantities.Using photon picture of light, show how Einstein’s photoelectric equation can be established. Write two features of photoelectric effect which cannot be explained by wave theory.Draw graphs showing variation of photoelectric current with applied voltage for two incident radiations of equal frequency and different intensities. Mark the graph for the radiation of higher intensity.ANSWER OF THREE MARKS QUESTIONS:We have given work function W=0 ,so using Einestein photoelectric equation1/2mv2=hν- W=hν1/2mv2=hc/λOr, mv=√2mhc/ λ (1)de -Broglie equation for emitted photoelectronsλ 1=h/mvusing equation (1)λ =(2mc/h) λ 21 (proved)742950180975From Einstein Photo electric equation the slope of this graph is h/e i.e. Planck constant divided by electronic charge. The intercept of this graph is W/e i.e. work function divided by electronic charge. Features of photoelectric effect cannot be explained on the basis of wave theory:a) Maximum kinetic energy of emitted photoelectrons each independent of intensity of light.b) There exists a minimum frequency i.e. threshold frequency for each photosensitive material below which no photo emission is possible. c) Photoelectric effect is instantaneous in nature. The properties of photon used to write Einstein’s photoelectric equation are The rest mass of the photon is zero. The energy of the photon is E = h.Curve 1 and 3 and curves 2 and 4 corresponds to different materials. For a given frequency of incident radiation the stopping potential is independent of intensity of light. As the pair of curves: 1&3 and 2 & 4 have different stopping potential so those materials are different.(i) As we increase the intensity of radiation the number of photons increases. And we know that each photon will impart energy to each electron hence the number of electron increases so that the photo-current.ii) On increasing the frequency above threshold frequency, only the energy of the photons increases not their numbers. Hence the photo- current will remain almost constant.With an increase in the accelerating potential, the photoelectric current increases first, reaches maximum when all the electrons gets collected at the positive potential plate and then remains constant. The maximum value of the anode current is called saturation current.The properties of photon used to write Einstein’s photoelectric equation are (i) The rest mass of the photon is zero. (ii) The energy of the photon is E = h.Stopping potential: For a particular frequency of incident radiation, the minimum negative (retarding) potential V0 for which the photocurrent stops or becomes zero is called the cut-off or stopping potential. Threshold frequency: The minimum frequency required for photoelectrons to be emitted from a metal surface is called the threshold frequency. The graph between stopping potential and frequency of incident radiation is shown below:857250116840390525-3810022860010147308.115252520955 ................
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