Islamic University of Gaza



Chapter 1

Introduction

Problems

Q. 1 Calculate the value of Planck's constant given that the following kinetic energies were observed for photo ejected electrons irradiated by radiation of the wavelengths noted.

|(/nm |320 |330 |345 |360 |385 |

|Ek/eV |1.17 |1.05 |0.885 |0.735 |0.511 |



Q. 2 How many photons does a monochromatic (single frequency) infrared rangefinder of power 1 mW and wavelength 1000 nm emit in 0.1 s?

Q. 3 Calculate (a) the wavelength of a neutron with a translational kinetic energy equal to kT at 300 K, (b) a tennis ball of mass 57 g travelling at 80 km/h.

Q. 4 To what speed must an electron be accelerated for it to have a wavelength of 3.0 cm?

Q. 5 Calculate the energy per photon and the energy per mole of photons for radiation of wavelength (a) 600 nm (red), (b) 550 nm (yellow), (c) 400 nm (blue).

Q. 6 A sodium lamp emits yellow light (550 nm). How many photons does it emit each second if its power is (a) 1.0 W, (b) 100 W?

Q. 7 The work function for metallic cesium is 2.14 eV. Calculate the kinetic energy and the speed of the electrons ejected by light of wavelength (a) 700 nm, (b) 300 nm.

Q. 8 Calculate the de Broglie wavelength of (a) a mass of 1.0 g travelling at 1.0 cm s-1, (b) the same, travelling at 100 km s-1, (c) an He atom travelling at 1000 m s-1 (a typical speed at room temperature).

Q. 9 Calculate the de Broglie wavelength of an electron accelerated from rest through a potential difference of (a) 100 V, (b) 1.0 kV, (c) 100 kV.

Q. 10 Demonstrate that the Planck distribution reduces to the Rayleigh-Jeans law at long wavelengths.

Q. 11 Use the Planck distribution to deduce the Stefan-Boltzmann law that the total energy density of black-body radiation is proportional to T4, and find the constant of proportionality.

Q. 12 At what wavelength does the maximum in the energy-density distribution function for a blackbody occur if (a) T=300 K? (b) T=3000 K? (c) T=10,000 K?

Q. 13 Sirius, one of the hottest known stars, has approximately a blackbody spectrum with (max = 2600 Å. Estimate the surface temperature of Sirius.

Q. 14 The work function of nickel equals 5.0 eV. Find (a) the threshold wavelength for nickel and (b) the maximum electron speed for a wavelength of 195 nm.

Q. 15 Consider the metals lithium, beryllium, and mercury, which have work functions of 2.3 eV, 3.9 eV, and 4.5 eV, respectively. If light of wavelength 300 nm is incident on each of these metals, determine (a) which metals exhibit the photoelectric effect and (b) the maximum kinetic energy for the photoelectron in each case.

Q. 16 Light of wavelength 500 nm is incident on a metallic surface. If the stopping potential for the photoelectric effect is 0.45 V, find (a) the maximum energy of the emitted electrons, (b) the work function, and (c) the cutoff wavelength.

Q. 17 A light source of wavelength illuminates a metal and ejects photoelectrons with a maximum kinetic energy of 1.00 eV. A second light source with half the wavelength of the first ejects photoelectrons with a maximum kinetic energy of 4.00 eV. What is the work function of the metal?

Q. 18 The following data are found for photoemission from calcium:

[pic]

Plot Vs versus (, and from the graph obtain Planck’s constant, the threshold frequency, and the work function for calcium.

Q. 19 A photon has a frequency of 6.0 × 104 Hz. (a) Convert this frequency into wavelength (nm). Does this frequency fall in the visible region? (b) Calculate the energy (in joules) of this photon. (c) Calculate the energy (in joules) of 1 mole of photons all with this frequency.

Q. 20 Explain why elements produce their own characteristic colors when they emit photons?

Q. 21 The first line of the Balmer series occurs at a wavelength of 656.3 nm. What is the energy difference between the two energy levels involved in the emission that result in this spectral line?

Q. 22 Calculate the frequency (Hz) and wavelength (nm) of the emitted photon when an electron drops from the n = 4 to the n = 2 level in a hydrogen atom. Calculate the ionization energy of the hydrogen atom.

Q. 23 An electron in the hydrogen atom makes a transition from an energy state of principal quantum numbers ni to the n = 2 state. If the photon emitted has a wavelength of 434 nm, what is the value of ni?

Q. 24 How does de Broglie’s hypothesis account for the fact that the energies of the electron in a hydrogen atom are quantized?

Q. 25(a) The energy required to remove an electron from sodium is 2.3 eV. Does sodium show a photoelectric effect for yellow light, with ( = 5890 Å? (b) What is the cutoff wavelength for photoelectric emission from sodium?

Q. 26 In a photoelectric experiment in which monochromatic light and a sodium photocathode are used, we find a stopping potential of 1.85 V for ( = 3000 Å and of 0.82 V for ( = 4000 Å. From these data determine (a) a value for Planck's constant, (b) the work function of sodium in electron volts, and (c) the threshold wavelength for sodium.

Q. 27 (a) Using Bohr's formula, calculate the three longest wavelengths in the Balmer series. (b) Between what wavelength limits does the Balmer series lie?

Q. 28 Calculate the shortest wavelength of the Lyman series lines in hydrogen. Of the Paschen series. Of the Pfund series. In what region of the electromagnetic spectrum does each lie?

Q. 29 How much energy is required to remove an electron from a hydrogen atom in a state with n = 8?

Q. 30 Calculate the radii of the first, second, and third Bohr orbits of hydrogen. (b) Find the electron’s speed in the same three orbits.

Q. 31 A hydrogen atom initially in its ground state (n=1) absorbs a photon and ends up in the state for which n=3. (a) What is the energy of the absorbed photon? (b) If the atom returns to the ground state, what photon energies could the atom emit?

Q. 32 A hydrogen atom is in its ground state (n= 1). Using the Bohr theory of the atom, calculate (a) the radius of the orbit, (b) the linear momentum of the electron, (c) the angular momentum of the electron, (d) the kinetic energy, (e) the potential energy, and (f) the total energy.

Q. 33 Find the temperature of a black body with a maximum in its spectral radiant emittance curve at a wavelength of 480 nm.

Q. 34 Assume that the surface temperature of the sun is 5800 K and that it radiates like a black body. Find the wavelength of maximum spectral radiant emittance. What color of visible light does this correspond to?

Q. 35 Calculate the speed of an electron in the n= 4 Bohr orbit and in the n =400 Bohr orbit of a hydrogen atom

Q. 36 Using the value of physical constants calculate RH and compare the result to its experimental value, 109,677.6 cm-1. Calculate the radii of the orbit in hydrogen atom with n= 2, 3, and 5.

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