- •Questions 23 and 24 pertain to the situation described below:
- •Section 29.4 The Momentum of a Photon and the Compton Effect
- •Section 29.5 The De Broglie Wavelength and the Wave Nature of Matter
- •Questions 46 and 47 pertain to the situation described below:
- •It is desired to obtain a diffraction pattern for electrons using a diffraction grating with lines separated by 10 nm. The mass of an electron is 9.11 1031 kg.
- •Section 29.6 The Heisenberg Uncertainty Principle
- •In which range is the fractional uncertainty, (px)/px , in the X component of its momentum?
Section 29.5 The De Broglie Wavelength and the Wave Nature of Matter
34. What kinetic energy must each neutron in a beam of neutrons have if their wavelength is 0.10 nm? The mass of a neutron is 1.67 1027 kg.
(a) 6.6 1019 J (c) 2.6 1020 J (e) 7.1 1020 J
(b) 1.3 1020 J (d) 6.3 1020 J
35. Approximately, what is the de Broglie wavelength of an electron that has been accelerated through a potential difference of 150 V? The mass of an electron is 9.11 1031 kg.
(a) 0.1 nm (c) 10 nm (e) 1000 nm
(b) 1 nm (d) 100 nm
36. Which experimental evidence confirms the hypothesis that matter exhibits wave properties?
(a) photoelectric experiments (d) Compton scattering experiments
(b) electron diffraction experiments (e) Michelson-Morley experiment
(c) Young's double-slit experiments
37. Complete the following statement: According to the de Broglie relation, the wavelength of a "matter" wave is inversely proportional to
(a) Planck's constant. (d) the frequency of the wave.
(b) the mass of the particle. (e) the speed of the particle.
(c) the momentum of the particle.
38. What is the de Broglie wavelength of an electron (m = 9.11 1031 kg) in a 5.0 103-volt X-ray tube?
(a) 0.007 nm (c) 0.017 nm (e) 0.034 nm
(b) 0.014 nm (d) 0.028 nm
39. Determine the de Broglie wavelength of a neutron (m = 1.67 1027 kg) that has a speed of 5.0 m/s.
(a) 79 nm (c) 395 nm (e) 1975 nm
(b) 162 nm (d) 529 nm
40. The de Broglie wavelength of an electron (m = 9.11 10–31 kg) is 1.2 10–10 m. Determine the kinetic energy of the electron.
(a) 1.5 10–15 J (c) 1.7 10–17 J (e) 1.9 10–19 J
(b) 1.6 10–16 J (d) 1.8 10–18 J
41. What is the kinetic energy of each electron in a beam of electrons if the beam produces a diffraction pattern of a crystal which is similar to that of a beam of 1.00 eV neutrons?
Note: The electron mass is 9.11 1031 kg; and the neutron mass is 1.67 1027 kg.
(a) 1830 eV (c) 3.35 106 eV (e) 2.34 102 eV
(b) 42.8 eV (d) 5.46 104 eV
42. What happens to the de Broglie wavelength of an electron if its momentum is doubled?
(a) The wavelength decreases by a factor of 4. (d) The wavelength increases by a factor of 2.
(b) The wavelength increases by a factor of 4. (e) The wavelength decreases by a factor of 2.
(c) The wavelength increases by a factor of 3.
43. The Hubble Space Telescope has an orbital speed of 7.56 103 m/s and a mass of 11 600 kg. What is the de Broglie wavelength of the telescope?
(a) 8.77 107 m (c) 6.63 1034 m (e) 7.56 1042 m
(b) 5.81 1026 m (d) 3.78 1040 m
44. A beam of electrons is incident on a single slit that has a width of 1.00 10–6 m and a diffraction pattern is observed on a screen located 15.0 m from the slit. The momentum of an individual electron in the beam is 5.91 10–24 kg m/s. What is the width of the central maximum fringe?
(a) 5.87 105 m (c) 6.67 104 m (e) 7.50 103 m
(b) 1.33 104 m (d) 3.37 103 m
45. In a computer monitor, electrons approach the screen at 1.20 108 m/s. What is the de Broglie wavelength of these electrons? Note: the mass of electrons is 9.109 1031 kg; and use the relativistic momentum in your calculation.
(a) 4.31 1012 m (c) 6.07 1012 m (e) 7.85 1012 m
(b) 5.56 1012 m (d) 6.62 1012 m