photons and matter waves

Chapter 38: PHOTONS AND MATTER WAVES

1. The units of the Planck constant h are those of:

A. energyB. powerC. momentumD. angular momentumE. frequency

2. If h is the Planck constant, then h is:

A. 2hB. 2hC. h/2D. h/2E. 2h/

3. The quantization of energy, E = nhf , is not important for an ordinary pendulum because:

A. the formula applies only to mass-spring oscillatorsB. the allowed energy levels are too closely spacedC. the allowed energy levels are too widely spacedD. the formula applies only to atomsE. the value of h for a pendulum is too large

4. The frequency of light beam A is twice that of light beam B. The ratio EA/EB of photonenergies is:

A. 1/2B. 1/4C. 1D. 2E. 4

5. The wavelength of light beam B is twice the wavelength of light beam B. The energy of aphoton in beam A is:

A. half the energy of a photon in beam BB. one-fourth the energy of a photon in beam BC. equal to the energy of a photon in beam BD. twice the energy of a photon in beam BE. four times the energy of a photon in beam B

574 Chapter 38: PHOTONS AND MATTER WAVES

6. A photon in light beam A has twice the energy of a photon in light beam B. The ratio pA/pBof their momenta is:

A. 1/2B. 1/4C. 1D. 2E. 4

7. Which of the following electromagnetic radiations has photons with the greatest energy?

A. blue lightB. yellow lightC. x raysD. radio wavesE. microwaves

8. Which of the following electromagnetic radiations has photons with the greatest momentum?

A. blue lightB. yellow lightC. x raysD. radio wavesE. microwaves

9. Rank following electromagnetic radiations according to the energies of their photons, from leastto greatest.

1. blue light2. yellow light3. x rays4. radio waves

A. 1, 2, 3, 4B. 4, 2, 1, 3C. 4, 1, 2, 3D. 3, 2, 1, 4E. 3, 1, 2, 4

10. The intensity of a uniform light beam with a wavelength of 500 nm is 2000W/m2. The photonflux (in number/m2 s) is about:A. 5 1017B. 5 1019C. 5 1021D. 5 1023E. 5 1025

Chapter 38: PHOTONS AND MATTER WAVES 575

11. The concentration of photons in a uniform light beam with a wavelength of 500 nm is 1.7 1013m3. The intensity of the beam is:A. 6.7 106W/m2B. 1.0 103W/m2C. 2.0 103W/m2D. 4.0 103W/m2E. 3.2 102W/m2

12. Light beams A and B have the same intensity but the wavelength associated with beam A islonger than that associated with beam B. The photon flux (number crossing a unit area perunit time) is:

A. greater for A than for BB. greater for B than for AC. the same for A and BD. greater for A than for B only if both have short wavelengthsE. greater for B than for A only if both have short wavelengths

13. In a photoelectric effect experiment the stopping potential is:

A. the energy required to remove an electron from the sampleB. the kinetic energy of the most energetic electron ejectedC. the potential energy of the most energetic electron ejectedD. the photon energyE. the electric potential that causes the electron current to vanish

14. In a photoelectric effect experiment at a frequency above cut off, the stopping potential isproportional to:

A. the energy of the least energetic electron before it is ejectedB. the energy of the least energetic electron after it is ejectedC. the energy of the most energetic electron before it is ejectedD. the energy of the most energetic electron after it is ejectedE. the electron potential energy at the surface of the sample

15. In a photoelectric effect experiment at a frequency above cut off, the number of electrons ejectedis proportional to:

A. their kinetic energyB. their potential energyC. the work functionD. the frequency of the incident lightE. the number of photons that hit the sample


16. In a photoelectric effect experiment no electrons are ejected if the frequency of the incidentlight is less than A/h, where h is the Planck constant and A is:

A. the maximum energy needed to eject the least energetic electronB. the minimum energy needed to eject the least energetic electronC. the maximum energy needed to eject the most energetic electronD. the minimum energy needed to eject the most energetic electronE. the intensity of the incident light

17. The diagram shows the graphs of the stopping potential as a function of the frequency of theincident light for photoelectric experiments performed on three different materials. Rank thematerials according to the values of their work functions, from least to greatest.

f

Vstop

...................................................................................................................................................................................................1

...................................................................................................................................................................................................2

...................................................................................................................................................................................................3

A. 1, 2, 3B. 3, 2, 1C. 2, 3, 1D. 2, 1, 3E. 1, 3, 2

18. The work function for a certain sample is 2.3 eV. The stopping potential for electrons ejectedfrom the sample by 7.0 1014-Hz electromagnetic radiation is:A. 0B. 0.60VC. 2.3VD. 2.9VE. 5.2V

19. The stopping potential for electrons ejected by 6.81014-Hz electromagnetic radiation incidenton a certain sample is 1.8V. The kinetic energy of the most energetic electrons ejected andthe work function of the sample, respectively, are:

A. 1.8 eV, 2.8 eVB. 1.8 eV, 1.0 eVC. 1.8 eV, 4.6 eVD. 2.8 eV, 1.0 eVE. 1.0 eV, 4.6 eV


20. Separate Compton effect experiments are carried out using visible light and x rays. Thescattered radiation is observed at the same scattering angle. For these experiments:

A. the x rays have the greater shift in wavelength and the greater change in photon energyB. the two radiations have the same shift in wavelength and the x rays have the greater change

in photon energyC. the two radiations have the same shift in wavelength and the visible light has the greater

change in photon energyD. the two radiations have the same shift in wavelength and the same change in photon energyE. the visible light has the greater shift in wavelength and the greater shift in photon energy

21. In Compton scattering from stationary particles the maximum change in wavelength can bemade smaller by using:

A. higher frequency radiationB. lower frequency radiationC. more massive particlesD. less massive particlesE. particles with greater charge

22. Of the following, Compton scattering from electrons is most easily observed for:

A. microwavesB. infrared lightC. visible lightD. ultraviolet lightE. x rays

23. In Compton scattering from stationary electrons the largest change in wavelength occurs whenthe photon is scattered through:

A. 0

B. 22.5

C. 45

D. 90

E. 180

24. In Compton scattering from stationary electrons the frequency of the emitted light is indepen-dent of:

A. the frequency of the incident lightB. the speed of the electronC. the scattering angleD. the electron recoil energyE. none of the above


25. In Compton scattering from stationary electrons the largest change in wavelength that canoccur is:

A. 2.43 1015mB. 2.43 1012mC. 2.43 109mD. dependent on the frequency of the incident lightE. dependent on the work function

26. Electromagnetic radiation with a wavelength of 5.71012m is incident on stationary electrons.Radiation that has a wavelength of 6.57 1012m is detected at a scattering angle of:A. 10

B. 121

C. 40

D. 50

E. 69

27. Electromagnetic radiation with a wavelength of 3.5 1012m is scattered from stationaryelectrons and photons that have been scattered through 50 are detected. An electron fromwhich one of these photons was scattered receives an energy of:

A. 0B. 1.1 1014 JC. 1.9 1014 JD. 2.3 1014 JE. 1.3 1013 J

28. Electromagnetic radiation with a wavelength of 3.5 1012m is scattered from stationaryelectrons and photons that have been scattered through 50 are detected. After a scatteringevent the magnitude of the electrons momentum is:

A. 0B. 1.5 1022 kg m/sC. 2.0 1022 kg m/sD. 2.2 1022 kg m/sE. 8.7 1023 kg m/s


29. Consider the following:

1. a photoelectric process in which some emitted electrons have kinetic energy greaterthan hf , where f is the frequency of the incident light.2. a photoelectric process in which all emitted electrons have energy less than hf .3. Compton scattering from stationary electrons for which the emitted light has a wave-length that is greater than that of the incident light.4. Compton scattering from stationary electrons for which the emitted light has a wave-length that is less than that of the incident light.

The only possible processes are:

A. 1B. 3C. 1 and 3D. 2 and 3E. 2 and 4

30. J. J. Thompsons measurement of e/m for electrons provides evidence of the:

A. wave nature of matterB. particle nature of matterC. wave nature of radiationD. particle nature of radiationE. transverse wave nature of light

31. Evidence for the wave nature of matter is:

A. electron diffraction experiments of Davisson and GermerB. Thompsons measurement of e/mC. Youngs double slit experimentD. the Compton effectE. Lenzs law

32. Which of the following is NOT evidence for the wave nature of matter?

A. The photoelectric effectB. The diffraction pattern obtained when electrons pass through a slitC. Electron tunnelingD. The validity of the Heisenberg uncertainty principleE. The interference pattern obtained when electrons pass through a two-slit system

33. Of the following which is the best evidence for the wave nature of matter?

A. The photoelectric effectB. The Compton effectC. The spectral radiancy of cavity radiationD. The relationship between momentum and energy for an electronE. The reflection of electrons by crystals


34. Monoenergetic electrons are incident on a single slit barrier. If the energy of each incidentelectron is increased the central maximum of the diffraction pattern:

A. widensB. narrowsC. stays the same widthD. widens for slow electrons and narrows for fast electronsE. narrows for slow electrons and widens for fast electrons

35. A free electron and a free proton have the same kinetic energy. This means that, compared tothe matter wave associated with the proton, the matter wave associated with the electron has:

A. a shorter wavelength and a greater frequencyB. a longer wavelength and a greater frequencyC. a shorter wavelength and the same frequencyD. a longer wavelength and the same frequencyE. a shorter wavelength and a smaller frequency

36. A free electron and a free proton have the same momentum. This means that, compared tothe matter wave associated with the proton, the matter wave associated with the electron:

A. has a shorter wavelength and a greater frequencyB. has a longer wavelength and a greater frequencyC. has the same wavelength and the same frequencyD. has the same wavelength and a greater frequencyE. has the same wavelength and a smaller frequency

37. A free electron and a free proton have the same speed. This means that, compared to thematter wave associated with the proton, the matter wave associated with the electron:

A. has a shorter wavelength and a greater frequencyB. has a longer wavelength and a greater frequencyC. has the same wavelength and the same frequencyD. has the same wavelength and a greater frequencyE. has a longer wavelength and a smaller frequency

38. Consider the following three particles:

1. a free electron with speed v02. a free proton with speed v03. a free proton with speed 2v0

Rank them according to the wavelengths of their matter waves, least to greatest.

A. 1, 2, 3B. 3, 2, 1C. 2, 3, 1D. 1, 3, 2E. 1, then 2 and 3 tied


39. Consider the following three particles:

1. a free electron with kinetic energy K02. a free proton with kinetic energy K03. a free proton with kinetic energy 2K0

Rank them according to the wavelengths of their matter waves, least to greatest.

A. 1, 2, 3B. 3, 2, 1C. 2, 3, 1D. 1, 3, 2E. 1, then 2 and 3 tied

40. A free electron has a momentum of 5.0 1024 kg m/s. The wavelength of its wave functionis:

A. 1.3 108mB. 1.3 1010mC. 2.1 1011mD. 2.1 1013mE. none of these

41. The frequency and wavelength of the matter wave associated with a 10-eV free electron are:

A. 1.5 1034 Hz, 3.9 1010mB. 1.5 1034 Hz, 1.3 1034mC. 2.4 1015 Hz, 1.2 109mD. 2.4 1015 Hz, 3.9 1010mE. 4.8 1015 Hz, 1.9 1010m

42. If the kinetic energy of a non-relativistic free electron doubles, the frequency of its wave functionchanges by the factor:

A. 1/2

B. 1/2C. 1/4D.

2

E. 2

43. A non-relativistic free electron has kinetic energy K. If its wavelength doubles, its kineticenergy is:

A. 4KB. 2KC. still KD. K/2E. K/4


44. The probability that a particle is in a given small region of space is proportional to:

A. its energyB. its momentumC. the frequency of its wave functionD. the wavelength of its wave functionE. the square of the magnitude of its wave function

45. (x) is the wave function for a particle moving along the x axis. The probability that theparticle is in the interval from x = a to x = b is given by:

A. (b) (a)B. |(b)|/|(a)|C. |(b)|2/|(a)|2D.

b

a(x) dx

E.b

a|(x)|2 dx

46. The significance of ||2 is:A. probabilityB. energyC. probability densityD. energy densityE. wavelength

47. Maxwells equations are to electric and magnetic fields as equation is to the wave functionfor a particle.

A. EinsteinsB. FermisC. NewtonsD. SchrodingersE. Bohrs

48. A free electron in motion along the x axis has a localized wave function. The uncertainty inits momentum is decreased if:

A. the wave function is made more narrowB. the wave function is made less narrowC. the wave function remains the same but the energy of the electron is increasedD. the wave function remains the same but the energy of the electron is decreasedE. none of the above


49. The uncertainty in position of an electron in a certain state is 5 1010m. The uncertainty inits momentum might be:

A. 5.0 1024 kg m/sB. 4.0 1024 kg m/sC. 3.0 1024 kg m/sD. all of the aboveE. none of the above

50. The reflection coefficient R for a certain barrier tunneling problem is 0.80. The correspondingtransmission coefficient T is:

A. 0.80B. 0.60C. 0.50D. 0.20E. 0

51. An electron with energy E is incident upon a potential energy barrier of height Epot > E andthickness L. The transmission coefficient T :

A. is zeroB. decreases exponentially with LC. is proportional to 1/LD. is proportional to 1/L2

E. is non-zero and independent of L

52. In order to tunnel through a potential barrier a particle must:

A. have energy greater than the barrier heightB. have spinC. be massiveD. have a wavelength longer than the barrier widthE. none of the above

53. An electron with energy E is incident on a potential energy barrier of height Epot and thicknessL. The probability of tunneling increases if:

A. E decreases without any other changesB. Epot increases without any other changesC. L decreases without any other changesD. E and Epot increase by the same amountE. E and Epot decrease by the same amount


54. Identical particles, each with energy E, are incident on the following four potential energybarriers:

1. barrier height = 5E, barrier width = 2L2. barrier height = 10E, barrier width = L3. barrier height = 17E, barrier width = L/24. barrier height = 26E, barrier width = L/3

Rank the barriers in terms of the probability that the particles tunnel through them, from leastprobability to greatest probability.

A. 1, 2, 3, 4B. 4, 3, 2, 1C. 1 and 2 tied, then 3, then 4D. 2, then 1 and 3 tied, then 4E. 3, 2, 1, 4


photons and matter waves

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