MULTIPLE CHOICE PROBLEMS for the STUDY of QUANTUM THEORY and ATOMIC PHYSICS

Transcription

1 MULTIPLE CHOICE PROBLEMS for the STUDY of QUANTUM THEORY and ATOMIC PHYSICS MC QUANTUM THEORY 1 SPANGLER 11/20/2014

2 MULTIPLE CHOICE PROBLEMS for the STUDY of QUANTUM THEORY and ATOMIC PHYSICS h = 6.63x10-34 Js = 4.14 X evs hc 2x10-25 Jm 1eV=1e x 1V=1.6x10-19 x 1V =1.6x10-19 J Mass in Kg: Proton x Electron X Neutron X PHOTONS and the PHOTOELECTRIC EFFECT 2. WAVE - PARTICLE DUALITY Photons 10. The graph shows the variation in radiation intensity per unit wavelength versus wavelength for a perfect blackbody at temperature T. Complete the following statement: As the blackbody temperature is increased, the peak in intensity of this curve A) Will remain constant. B) Will be shifted to longer wavelengths and its magnitude will increase. C) Will be shifted to shorter wavelengths and its magnitude will increase. D) Will be shifted to longer wavelengths and its magnitude will decrease. E) Will be shifted to shorter wavelengths and its magnitude will decrease. 1. Light is usually thought of as wave-like in nature and electrons as particle-like. In which one of the following activities does light behave as a particle or does an electron behave as a wave? A) A Young's double slit experiment is conducted using blue light. B) X-rays are used to examine the crystal structure of sodium chloride. C) Water is heated to its boiling point in a microwave oven. D) An electron enters a parallel plate capacitor and is deflected downward. E) A beam of electrons is diffracted as it passes through a narrow slit. 2. Upon which one of the following parameters does the energy of a photon depend? A) Mass B) Amplitude C) Polarization D) Frequency E) Phase relationships 3. For which one of the following problems did Max Planck make contributions that eventually led to the development of the "quantum" hypothesis? A) Photoelectric effect B) Uncertainty principle C) Blackbody radiation curves D) The motion of the earth in the ether E) The invariance of the speed of light through vacuum 4. Determine the energy of a single photon in a beam of light of wavelength 450 nm. A) 2.0 ev B) 2.5 ev C) 2.8 ev D) 4.2 ev E) 4.5 ev 5. A laser emits a single, 2.0 ms pulse of light that has a frequency of 2.83 x Hz and a total power of W. How many photons are in the pulse? A) B) 1.6 x10 24 C) D) E) MC QUANTUM THEORY 2 SPANGLER 11/20/2014

3 6. A laser emits a pulse of light with energy 5000 J. Determine the number of photons in the pulse if the wavelength of light is 480 nm. A) B) C) D) E) A laser emits photons of energy 2.5 ev with a power of 10-3 W. How many photons are emitted in one second? A) 4.0 x B) C) D) E) An X-ray generator produces photons with energy ev or less. Which one of the following phrases most accurately describes the wavelength of these photons? A) nm or longer D) 0.25 nm or shorter B) nm or longer E) 0.75 nm or shorter C) 0.75 nm or longer 9. A laser produces 3.0 W of light at wavelength 600 nm. How many photons per second are produced? A) 7.3 x B) C) D) E) Complete the following statement: The photon description of light is necessary to explain A) Polarization D) Electron diffraction B) Photoelectric effect E) Interference of light C) Diffraction of light 12. Which one of the following phrases best describes the term work function? A) The minimum energy required to vaporize a metal B) The work required to place a charged particle on a metal surface C) The minimum energy required to remove electrons from the metal D) The minimum energy required to remove an atom from a metal surface E) The work done by electromagnetic radiation when it hits a metal surface 13. Which one of the following quantities is the same for all photons in vacuum? A) Speed B) Frequency C) Kinetic energy D) Wavelength E) Total energy 14. Complete the following statement: The term photon applies A) Only to X-rays. B) Only to visible light. C) To any form of wave motion. D) To any form of particle motion. E) To any form of electromagnetic radiation. MC QUANTUM THEORY 3 SPANGLER 11/20/2014

4 15. Which type of wave motion does not involve photons? A) Gamma rays D) Infrared radiation B) Microwaves E) Sound waves C) Radio waves 16. Which one of the following statements concerning photons is false? A) Photons have zero mass. B) The rest energy of all photons is zero. C) Photons travel at the speed of light in a vacuum. D) Photons have been brought to rest by applying a strong magnetic field to them. E) The energy of a photon is proportional to its frequency. The Photoelectric Effect 17. Photons of what minimum frequency are required to remove electrons from gold? Note: The work function for gold is 4.8 ev. A) Hz D) Hz B) Hz E) Hz C) Hz 18. Photons of energy 6 ev cause electrons to be emitted from a certain metal with a maximum kinetic energy of 2 ev. If photons of 2X the wavelength are incident on this metal which one of the following statements is true? A) No electrons will be emitted. B) Electrons will be emitted with a maximum kinetic energy of 1 ev. C) Electrons will be emitted with a maximum kinetic energy of 8 ev. D) Electrons will be emitted with a maximum kinetic energy of 10 ev. E) Electrons will be emitted with a maximum kinetic energy of 20 ev. 19. White light consisting of wavelengths 380 nm to 750 nm is incident on a lead surface. For which one of the following ranges of wavelengths will photoelectrons be emitted from the lead surface, W 0 = 6.63x10-19 J? A) 380 nm to 750 nm D) 380 nm to 410 nm B) 380 nm to 630 nm E) No photoelectrons will be emitted. C) 380 nm to 540 nm 20. When ultraviolet photons with a wavelength of 3.45 x 10-7 m are incident on an unknown metal surface in a vacuum, electrons with a maximum kinetic energy of 1.52 ev are emitted from the surface. What is the work function of the metal? A) 3.60 ev B) 3.11 ev C) 2.59 ev D) 2.08 ev E) 1.98 ev 21. Photons of energy 5.0 ev strike a metal whose work function is 3.5 ev. Determine which one of the following best describes the kinetic energy of the emitted electrons. A) 1.5 ev or less D) 3.5 ev or more B) 1.5 ev or more E) 3.5 ev or less C) 2.5 ev or more MC QUANTUM THEORY 4 SPANGLER 11/20/2014

5 22. The work function for a particular metal is 4.0 ev. Which one of the following best describes the wavelength of electromagnetic radiation needed to eject electrons from this metal? A) 310 nm or greater D) 620 nm or smaller B) 310 nm or smaller E) 800 nm or greater C) 620 nm or greater Use the following to answer questions 23-24: A physicist wishes to produce electrons by shining light on a metal surface. The light source emits light with a wavelength of 450 nm. The table lists the only available metals and their work functions. 23. Which metal(s) can be used to produce electrons by the photoelectric effect? A) Barium only D) Barium or lithium B) Tungsten only E) Lithium, tantalum, or tungsten C) Tungsten or tantalum 24. Which entry in the table below correctly identifies the metal that will produce the most energetic electrons and their energies? Metal Maximum electron energy observed A) Lithium 2.30 ev B) Lithium 0.46 ev C) Tungsten 1.75 ev D) Tungsten 2.75 ev E) Tungsten 4.50 ev MC QUANTUM THEORY 5 SPANGLER 11/20/2014

6 The MOMENTUM of a PHOTON and the COMPTON EFFECT 25. A digital wireless telephone communicates via microwaves that have a frequency of 1930 MHz. What are the momentum and energy for the microwave photons emitted by the telephone? Photon momentum photon energy A) kg m/s J B) kg m/s J C) kg m/s J D) kg m/s J E) kg m/s J 26. In the Compton effect, a photon of wavelength l and frequency f hits an electron that is initially at rest. Which one of the following occurs as a result of the collision? A) The photon is absorbed completely. B) The photon gains energy, so the final photon has a frequency greater than f. C) The photon gains energy, so the final photon has a wavelength greater than. D) The photon loses energy, so the final photon has a frequency less than f. E) The photon loses energy, so the final photon has a wavelength less than. 27. Which one of the following is demonstrated by the Compton effect? A) Time dilation B) Length contraction C) The uncertainty principle D) Electrons have wave properties E) Electromagnetic radiation has particle properties 28. Complete the following statement: The photon or "particle" theory of electromagnetic radiation is necessary to explain the A) Refraction of light by a prism. B) Diffraction of light by a grating. C) Reflection of light from a mirrored surface. D) Results of Compton scattering experiments. E) Interference of light in Young's double-slit experiment. 29. In the Compton scattering experiment shown in the figure, a monochromatic beam of X-rays strikes a target containing free electrons. Scattered X-rays are detected with a wavelength of m at an angle of 45 away from the original beam direction. What is the wavelength of the incident monochromatic Xrays? A) 3.21 x m D) m B) m E) m C) m 30. What is the speed of an electron that has the same momentum as a photon with a wavelength (in a vacuum) of 380 nm? A) m/s D) m/s B) m/s E) m/s C) m/s MC QUANTUM THEORY 6 SPANGLER 11/20/2014

7 31. A photon of wavelength 200 nm is scattered by an electron that is initially at rest. Which one of the following statements concerning the wavelength of the scattered photon is true? A) The wavelength is zero nm. B) The wavelength is 200 nm. C) The wavelength is 100 nm. D) The wavelength is greater than 200 nm. E) The wavelength is less than 200 nm, but greater than zero. 32. Incident X-rays in a Compton scattering experiment have a wavelength of nm. Determine the wavelength of the scattered X-rays that are detected at an angle of The Compton wavelength of the electron is m. A) nm B) nm C) nm D) nm E) nm 33. A photon has a collision with a stationary electron (h/mc = m) and loses 5.0% of its energy. The photon scattering angle is 180. What is the wavelength of the incident photon in this scattering process? A) m D) m B) m E) m C) m 34. What kinetic energy must a beam of neutrons have if their wavelength is 0.10 nm? A) J D) J B) J E) J C) J X-RAY PRODUCTION 58. Which one of the following statements concerning the cutoff wavelength exhibited in X-ray spectra is true? A) The cutoff wavelength depends on the target material. B) The cutoff wavelength depends on the potential difference across the X-ray tube. C) The cutoff wavelength is independent of the energy of the incident electrons. D) The cutoff wavelength occurs because of the mutual shielding effects of K-shell electrons. E) The cutoff wavelength occurs because an incident electron cannot give up all of its energy. 59. In an X-ray tube, electrons with energy 35 kev are incident on a cobalt (Z = 27) target. Determine the cutoff wavelength for X-ray production. A) m D) m B) m E) m C) m 60. Which electron energy will produce the lowest cutoff wavelength for X-ray production from a nickel (Z = 28) surface? A) 25 kev B) 30 kev C) 35 kev D) 40 kev E) 45 kev MC QUANTUM THEORY 7 SPANGLER 11/20/2014

8 62. Electrons in an X-ray tube are accelerated through a potential difference of 40 kv. The electrons then strike a zirconium (Z = 40) target. Determine the cutoff frequency for X-ray production. A) Hz D) Hz B) Hz E) Hz C) Hz 63. What is the operating voltage of a medical X-ray machine that has a cut-off wavelength of m? A) V B) V C) V D) V E) V The De BROGLIE WAVELENGTH and the WAVE NATURE of MATTER 35. Approximately, what is the de Broglie wavelength of an electron that has been accelerated through a potential difference of 150 V? A) 0.1 nm B) 1 nm C) 10 nm D) 100 nm E) 1000 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 in a 5.0 x 10 3 volt X-ray tube? A) nm B) nm C) nm D) nm E) nm 39. Determine the de Broglie wavelength of a neutron which has a speed of 5.0 m/s. A) 79 nm B) 162 nm C) 395 nm D) 529 nm E) 1975 nm MC QUANTUM THEORY 8 SPANGLER 11/20/2014

9 40. The de Broglie wavelength of an electron is m. Determine the kinetic energy of the electron. A) J D) J B) J E) J C) J 41. What is the kinetic energy that a beam of electrons must have if it is to produce a diffraction pattern of a crystal which is similar to that of a beam of 1.00 ev neutrons? is kg. A) 1830 ev D) ev B) 42.8 ev E) ev C) 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. B) The wavelength increases by a factor of 4. C) The wavelength increases by a factor of 3. D) The wavelength increases by a factor of 2. E) The wavelength decreases by a factor of The Hubble Space Telescope has an orbital speed of 7.56 x 10 3 m/s and a mass of kg. What is the de Broglie wavelength of the telescope? A) m D) m B) m E) m C) m Use the following to answer questions 46-47: It is desired to obtain a diffraction pattern for electrons using a diffraction grating with lines separated by 10 nm. 46. What is the approximate kinetic energy of electrons that would be diffracted by such a grating? A) ev D) ev B) ev E) ev C) ev 47. Suppose it is desired to observe diffraction effects for a beam of electromagnetic radiation using the same grating. Roughly, what is the required energy of the individual photons in the beam? A) 10-6 ev B) 10-4 ev C) 10-2 ev D) 10 2 ev E) 10 4 ev MC QUANTUM THEORY 9 SPANGLER 11/20/2014

10 LINE SPECTRA, BOHR MODEL of H 2, De BROGLIE'S EXPLANATION 5. Each atom in the periodic table has unique set of spectral lines. Which one of the following statements is the best explanation for this observation? A) Each atom has a dense central nucleus. B) The electrons in atoms orbit the nucleus. C) Each atom has a unique set of energy levels. D) The electrons in atoms are in constant motion. E) Each atom is composed of positive and negative charges. 6. Each atom in the periodic table has a unique set of spectral lines. The model of atomic structure that provides the best explanation for this observation was proposed by A) Balmer. B) Bohr. C) Einstein. D) Rutherford. E) Thomson. 7. Which one of the following pairs of characteristics of light is best explained by assuming that light can be described in terms of photons? A) Photoelectric effect and the effect observed in Young's experiment B) Diffraction and the formation of atomic spectra C) Polarization and the photoelectric effect D) Existence of line spectra and the photoelectric effect E) Polarization and the formation of line spectra 8. Which one of the following statements is the assumption that Niels Bohr made about the angular momentum of the electron in the hydrogen atom? A) The angular momentum of the electron is zero. B) The angular momentum can assume only certain discrete values. C) Angular momentum is not quantized. D) Angular momentum can assume any value greater than zero because it's proportional to the radius of the orbit. E) The angular momentum is independent of the mass of the electron. 9. Why was it necessary to Bohr to require that electrons remain in stationary orbits? A) An electron must travel in a circular path. B) It was required by the Heisenberg uncertainty principle. C) No two electrons can be in the same region in the atom. D) It was required by the Pauli exclusion principle. E) Classical physics predicts that the electron should spiral into the nucleus. 10. Complete the following statement: For the ground state of the hydrogen atom, the Bohr model correctly predicts A) Only the energy. B) Only the angular momentum. C) Only the angular momentum and the spin. D) The angular momentum and the energy. E) The energy, the angular momentum, and the spin. 11. Complete the following statement: An individual copper atom emits electromagnetic radiation with wavelengths that are A) Evenly spaced across the spectrum. B) Unique to that particular copper atom. C) The same as other elements in the same column of the periodic table. D) Unique to all copper atoms. E) The same as those of all elements. MC QUANTUM THEORY 10 SPANGLER 11/20/2014

11 12. Electrons have been removed from a beryllium atom (Z = 4) until only one remains. Determine the energy of the photon that can be emitted if the remaining electron is in the n = 2 level. A) 13.6 ev B) 54.4 ev C) 122 ev D) 163 ev E) 218 ev 13. Determine the wavelength of incident electromagnetic radiation required to cause an electron transition from the n = 6 to the n = 8 level in a hydrogen atom. A) nm D) nm B) nm E) nm C) nm 14. The 2 nd ionization energy (the energy required to remove the second outermost electron) of calcium is 11.9 ev. Determine the maximum wavelength of incident radiation that can be used to remove the second electron from a calcium atom? A) 16.6 nm B) 52 nm C) 104 nm D) 208 nm E) 416 nm 15. Which one of the following is an electron transition from the n = 4 level to the n = 7 level in a hydrogen atom? A) Emission of a 0.28 ev photon D) Absorption of a 0.28 ev photon B) Emission of a 0.57 ev photon E) Absorption of a 0.57 ev photon C) Emission of a 0.85 ev photon 16. Determine the maximum wavelength of incident radiation that can be used to remove the remaining electron from a singly ionized helium atom He + (Z = 2). Assume the electron is in its ground state. A) 6.2 nm B) 12.4 nm C) 22.8 nm D) 45.6 nm E) 54.4 nm 17. What is the longest wavelength in the Paschen series of atomic spectra? A) m D) m B) m E) m C) m 18. Determine the energy of the photon emitted when the electron in a hydrogen atom undergoes a transition from the n = 8 level to the n = 6 level. A) 0.17 ev B) 0.21 ev C) 0.36 ev D) 0.57 ev E) 13.4 ev MC QUANTUM THEORY 11 SPANGLER 11/20/2014

12 19. The kinetic energy of the ground state electron in hydrogen is ev. What is its potential energy? A) ev B) ev C) ev D) ev E) zero ev 20. An electron is in the ground state of a hydrogen atom. A photon is absorbed by the atom and the electron is excited to the n = 2 state. What is the energy in ev of the photon? A) 13.6 ev B) 10.2 ev C) 3.40 ev D) 1.51 ev E) 0.54 ev 21. In the Bohr model, what is the radius of a hydrogen atom when its electron is excited to the n = 9 state? A) m D) m B) m E) m C) m 22. Determine the kinetic energy of an electron that has a de Broglie wavelength equal to twice the diameter of the hydrogen atom. Assume that the hydrogen atom is a sphere of radius m. A) 13.6 ev B) 27.2 ev C) 33.6 ev D) 48.9 ev E) 65.2 ev 23. What is the shortest possible wavelength in the Lyman series for atomic hydrogen? A) 91.2 nm B) 104 nm C) 122 nm D) 364 nm E) 820 nm 24. The electron in a hydrogen atom is in the n = 3 state. What is (are) the possible value(s) for an emitted photon? A) 1.89 ev or ev D) 0.66 ev or ev B) 1.89 ev or 13.6 ev E) 1.51 ev only C) 0.66 ev or 13.6 ev 25. What energy (in ev) is required to remove the remaining electron from a singly ionized helium atom, He + (Z = 2)? A) 3.40 ev B) 13.6 ev C) 27.2 ev D) 54.4 ev E) 76.9 ev MC QUANTUM THEORY 12 SPANGLER 11/20/2014

13 Use the following to answer questions 72-78: The figure shows an energy level diagram for the hydrogen atom. Several transitions are shown and are labeled by letters. 72. In which transition is a Balmer series photon absorbed? A) A B) B C) C D) D E) E 74. Determine the energy of the photon involved in transition E. A) 1.5 ev B) 1.9 ev C) 3.4 ev D) 10.2 ev E) 12.1 ev 73. Which transition corresponds to the absorption of the photon with the longest wavelength? A) A B) B C) C D) D E) E 75. Determine the wavelength of the radiation involved in transition B. A) 291 nm B) 364 nm C) 487 nm D) 652 nm E) 1910 nm 76. Which transition will occur when a hydrogen atom is irradiated with radiation of wavelength 103 nm? A) A B) B C) C D) D E) E 77. Which transition will occur when a hydrogen atom is irradiated with radiation of frequency Hz? A) A B) B C) C D) D E) E 78. Which transition involves the longest wavelength line in the visible portion of the hydrogen spectrum? A) A B) B C) C D) D E) E MC QUANTUM THEORY 13 SPANGLER 11/20/2014

14 QUANTUM MECHANICAL H According to the quantum mechanical picture of the atom, which one of the following is a true statement concerning the ground state electron in a hydrogen atom? A) The ground state electron has zero kinetic energy. B) The ground state electron has zero binding energy. C) The ground state electron has zero ionization energy. D) The ground state electron has zero spin angular momentum. E) The ground state electron has zero orbital angular momentum. The PAULI EXCLUSION PRINCPLE 37.To which model of atomic structure does the Pauli exclusion principle apply? A) The nuclear atom D) the plum-pudding model B) The quantum mechanical atom E) the planetary model C) The billiard ball atom 45. Name the physicist credited with the following statement: No two electrons in an atom can have the same set of values for the four quantum numbers. A) Werner Heisenberg D) Niels Bohr B) Wolfgang Pauli E) Erwin Schrödinger C) Arthur Compton APPLICATIONS 64. Complete the following sentence: In the condition known as population inversion, A) The amount of one type of gas atoms is larger than that of another in a mixture. B) The number of energy levels that are populated is larger than that of unpopulated levels. C) There are more electrons occupying lower energy levels than occupying higher energy levels. D) There are more electrons occupying higher energy levels than occupying lower energy levels. E) There are more photons than electrons in a given system. 65. An argon-ion laser emits a blue-green beam of light with a wavelength of 488 nm in a vacuum. What is the difference in energy in joules between the two energy states for the atomic transition that produces this light? A) J D) J B) J E) J C) J 66. A pulsed laser has an average output power of 4 W. Each pulse consists of light at wavelength 500 nm and has a 25 ms duration. How many photons are emitted in a single pulse? A) B) C) D) E) MC QUANTUM THEORY 14 SPANGLER 11/20/2014

15 Answer Key 1. PHOTONS and the PHOTOELECTRIC EFFECT 2. WAVE - PARTICLE DUALITY 1. E 2. D 3. C 4. C 5. A 6. C 7. B 8. A 9. E 10. C 11. B 12. C 13. A 14. E 15. E 16. D 17. B 18. A 19. E 20. D 21. A 22. B 23. D 24. B 25. B 26. D 27. E 28. D 29. E 30. A 31. D 32. D 33. C 34. B 35. A 36. B 37. C 38. C 39. A 40. C 41. A 42. E 43. E 46. C 47. D 58. B 59. E 60. E 61. C 62. B 63. E LINE SPECTRA, BOHR MODEL of H 2 5. C 6. B 7. D 8. B 9. E 10. A 11. D 12. D 13. E 14. C 15. E 16. C 17. B 18. A 19. C 20. B 21. D 22. C 23. A 24. A 25. D 26. E 37. B 45. B 64. D 65. A 66. B 72. E 73. C 74. B 75. C 76. D 77. C 78. E MC QUANTUM THEORY 15 SPANGLER 11/20/2014