Exam

Name___________________________________

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

1) An electron has the same de Broglie wavelength as an 810-nm photon. The speed of the electronis closest to:A) 720 m/s B) 900 m/s C) 990 m/s D) 800m/s E) 260 m/s

1)

2) A proton has a speed of 2.3 ! 104 m/s. The energy of a photon that has the same de Brogliewavelength as the proton is closest to:A) 49 keV B) 120 keV C) 72 keV D) 140 keV E) 95 keV

2)

3) An electron has the same de Broglie wavelength as a 1.3-eV photon. The speed of the electron isclosest to:A) 660 m/s B) 600 m/s C) 710 m/s D) 760 m/s E) 550 m/s

3)

4) An electron has a kinetic energy of 5.4 eV. The energy of a photon that has the same de Brogliewavelength as the electron is closest to:A) 2.5 keV B) 2.3 keV C) 2.7 keV D) 2.2 keV E) 2.0 keV

4)

5) The neutrons in a beam have energies ranging from 0.04 eV to 0.14 eV. The beam is incidentnormally on the surface of a crystal. The neutrons diffract from surface planes of the crystalwhose spacing is 189 pm. The range of angles from the normal, at which maximum intensity ofdiffracted neutrons occurs, is closest to:A) 19° to 49°B) 15° to 51°C) 19° to 51°D) 24° to 51°E) 24° to 49°

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6) The neutrons in a beam have energies ranging from 0.02 eV to 0.17 eV. The beam is incidentnormally on the surface of a crystal. The neutrons diffract from surface planes of the crystalwhose spacing is 287 pm. Neutrons diffracted at an angle of 22° from the normal are allowed topass through slits to form a new beam. The energy of the neutrons in this new beam is closest to:A) 0.061 eV B) 0.052 eV C) 0.071 eV D) 0.044 eV E) 0.037 eV

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7) A 350-eV electron beam is directed normally at the surface of a crystal. The first order intensitymaximum of diffracted electrons occurs at an angle of 17° from the normal. The spacing of thesurface planes of the crystal is closest to:A) 150 pm B) 220 pm C) 200 pm D) 180 pm E) 130 pm

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8) A 630-eV electron beam is directed normally at the surface of a crystal. The first-order intensitymaximum of diffracted electrons occurs at an angle of 12° from the normal. The angle from thenormal of the second-order intensity maximum is closest to:A) 19° B) 27° C) 23° D) 21° E) 25°

8)

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9) The spacing of the surface planes of a crystal is 287 pm. A beam directed normally at the surfaceof the crystal undergoes first-order diffraction at an angle of 18° from the normal. The diffractionis done with a beam of monochromatic x-rays. The energy of the photons is closest to:A) 17 keV B) 15 keV C) 16 keV D) 13 keV E) 14 keV

9)

10) The spacing of the surface planes of a crystal is 233 pm. A beam directed normally at the surfaceof the crystal undergoes first-order diffraction at an angle of 61° from the normal. The diffractionis done with a beam of monoenergetic electrons. The energy of the electrons is closest to:A) 31 eV B) 22 eV C) 41 eV D) 36 eV E) 26 eV

10)

11) The spacing of the surface planes of a crystal is 278 pm. A beam directed normally at the surfaceof the crystal undergoes first-order diffraction at an angle of 44° from the normal. The diffractionis done with a beam of monoenergetic neutrons. The energy of the neutrons is closest to:A) 0.027 eV B) 0.030 eV C) 0.022 eV D) 0.019 eV E) 0.025 eV

11)

12) A single slit is illuminated at normal incidence with a parallel beam of 534-nm light. The entirecentral band of the diffraction pattern is observed at 90°. The illumination is replaced by a860-eV electron beam, which is directed at the slit at normal incidence. The angle at which thefirst minimum of the electron diffraction pattern occurs is closest to:A) 0.078 mradB) 0.099 mradC) 0.038 mradD) 0.12 mradE) 0.058 mrad

12)

13) A molecule of roughly spherical shape has a mass of 6.10 ! 10-25 kg and a diameter of 0.7 nm.The uncertainty in the measured position of the molecule is equal to the molecular diameter. Theminimum speed of the molecule is closest to:A) 2 m/sB) 20 m/sC) 0.002 m/sD) 0.02 m/sE) 0.2 m/s

13)

14) In the Davisson-Germer experiment in 1927, a beam of electrons was scattered off a crystal ofnickel. The intensity of the scattered beam varied with the angle of scattering, and analysis ofthese results lead to confirmation ofA) the wave nature of electrons.B) the Rutherford model of the nucleus.C) the Bohr model of the atom.D) the particle nature of light.E) the quantization of energy levels.

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15) Light of wavelength 105 nm falls on a metal surface for which the work function is 5.00 eV. h =

6.626 × 10-34 J ∙ s = 4.136 × 10-15 eV ∙ s, c = 3.00 × 108 m/s, 1.00 eV = 1.60 × 10-19 J. The minimum

de Broglie wavelength of the photoelectrons (of mass 9.11 × 10-31 kg) emitted from this metal isclosest to:A) 0.332 nm B) 0.939 nm C) 0.235 nm D) 0.470 nm E) 0.664 nm

15)

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16) An electron is confined to a length of 500 pm on the x-axis. The minimum kinetic energy of theelectron is closest to:A) 0.015 eVB) 0.15 eVC) 15 eVD) 1.5 eVE) 0.0015 eV

16)

17) A proton is confined to a length of 2.0 pm on the x-axis. The minimum kinetic energy of theproton is closest to:A) 0.5 eV B) 500 eV C) 50 eV D) 5 eV E) 5000 eV

17)

18) A laser produces a beam of 4000-nm light. A shutter allows a pulse of light, 30 ps in duration, topass. The uncertainty in the energy of a photon in the pulse is closest to:

A) 2 ! 10-5 eV

B) 2 ! 10-2 eV

C) 2 ! 10-3 eV

D) 2 ! 10-4 eV

E) 2 ! 10-6 eV

18)

19) An ultraviolet source produces a monochromatic beam of 200-nm light. A shutter allows a pulseto pass that is 10,000 wavelengths long. The uncertainty in the energy of a photon in this pulse isclosest to:

A) 10-6 eV B) 10-4 eV C) 10-2 eV D) 10-5 eV E) 10-3 eV

19)

20) A 440-nm spectral line is produced by a transition from an excited state to the ground state. Thenatural line width of the spectral line is 0.020 pm. The average time the atom spends in theexcited state is closest to:

A) 5 ! 10-9 s

B) 5 ! 10-6 s

C) 5 ! 10-10 s

D) 5 ! 10-7 s

E) 5 ! 10-8 s

20)

21) The ! (1530) particle has a rest energy of 1530 MeV and an energy width (uncertainty) of 9 MeV.The average lifetime of the ! (1530) particle is closest to:

A) 2 ! 10-22 s

B) 7 ! 10-22 s

C) 2 ! 10-23 s

D) 7 ! 10-24 s

E) 7 ! 10-23 s

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22) The !(1385) particle has a rest energy of 1385 MeV and its average lifetime is 1.9 x 10-23 s. Theenergy width (uncertainty) of the !(1385) particle is closest to:A) 0.35 MeV B) 35 MeV C) 11 MeV D) 1.1 MeV E) 3.5 MeV

22)

23) The kinetic energy of the neutrons, considered as nonrelativistic, in a neutron beam is 2.0 MeV.The de Broglie wavelength of the neutrons is closest to:

A) 3 ! 10-14 m

B) 6 ! 10-14 m

C) 5 ! 10-14 m

D) 11 ! 10-14 m

E) 2 ! 10-14 m

23)

24) The de Broglie wavelength of the electrons, considered as nonrelativistic, in the electron beam ofa television video tube is 7.55 pm. The accelerating potential used in the tube is closest to:A) 26 kV B) 20 kV C) 28 kV D) 22 kV E) 24 kV

24)

25) An electron microscope produces a beam of relativistic electrons whose de Broglie wavelength is4.0 pm. The accelerating potential at which the microscope operates is closest to:A) 87 keV B) 94 keV C) 84 keV D) 98 keV E) 91 keV

25)

26) A linear accelerator produces a beam of relativistic electrons that have a kinetic energy of 10MeV. The de Broglie wavelength of these electrons is closest to:A) 0.12 pm B) 0.59 pm C) 0.27 pm D) 0.39 pm E) 0.18 pm

26)

27) A major advantage of an electron microscope over a visible light microscope is that the electronmicroscopeA) operates with much lower intensity.B) can penetrate opaque samples.C) can have much better resolution.D) can form images of individual electrons.E) requires no lenses for its operation.

27)

28) A laser pulse of duration 25 ms has a total energy of 1.2 J. If the wavelength of this radiation is463 nm, how many photons are emitted in one pulse?A) 2.2 × 1017

B) 3.4 × 1019

C) 6.9 × 1019

D) 1.1 × 1017

E) 2.8 × 1018

28)

29) In a neutron gas, for the neutrons that are traveling at the root-mean-square speed to have a de

Broglie wavelength equal to the wavelength of light of frequency 2.40 × 1018 Hz, the temperatureof the gas would have to be closest to which of the following? (Boltzmann constant is 1.38 ×

10-23 J/K, neutron mass is 1.675 × 10-27 kg, Planck’s constant is 6.626 × 10-34 J ∙ s.)A) 300°C B) 405°C C) 132°C D) -71°C E) 13°C

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30) Helium atoms (of mass 6.65 × 10-27 kg) are at room temperature of 20.0°C. The Boltzmann

constant is 1.38 × 10-23 J/K and Planck’s constant is 6.626 × 10-34 J ∙ s. The de Broglie wavelengthof the atoms traveling at the root-mean-square speed is closest to:

A) 1.04 × 10-10 m

B) 3.99 × 10-10 m

C) 7.38 × 10-11 m

D) 5.22 × 10-11 m

E) 2.82 × 10-10 m

30)

Situation 39.1Nonrelativistic electrons pass through a slit 1.50-µm wide and then fall on a screen 1.20 m away. You observe thatelectrons strike the screen at the center point opposite the center of the slit, but the first points at which no electrons strike

the screen are ±1.73 cm from the center point. The mass of an electron is 9.11 × 10-31 kg, the speed of light is 3.00 × 108

m/s, and Planck’s constant is 6.626 × 10-34 J ∙ s.

31) In Situation 39.1, the wavelength of the electrons is closest to:A) 30.6 nm B) 43.3 nm C) 10.8 nm D) 21.6 nm E) 15.3 nm

31)

32) In Situation 39.1, the speed of the electrons as they approach the slit is closest to:A) 33.6 km/sB) 47.5 km/sC) 0.805 mVD) 23.8 km/sE) 16.8 km/s

32)

33) In Situation 39.1, the potential difference through which the electrons were accelerated from restis closest to:A) 0.805 mV B) 6.44 mV C) 3.22 mV D) 1.07 mV E) 1.61 mV

33)

34) In Situation 39.1, the kinetic energy of the electrons as they approach the slit is closest to:

A) 10.3 × 10-22 J

B) 5.15 × 10-22 J

C) 2.58 × 10-22 J

D) 1.29 × 10-22 J

E) 3.64 × 10-22 J

34)

35) The energy of a photon is equal to the kinetic energy of a nonrelativistic electron. Which one ofthe following statements is accurate?A) The de Broglie wavelength of the electron is equal to the wavelength of the photon.B) The electron and photon have the same speed.C) The momentum of the photon is equal to the momentum of the electron.D) All of the above statements are correct.E) None of the above statements are correct.

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36) The de Broglie wavelength of a nonrelativistic neutron is the same as the wavelength of aphoton. Which of the following statements about them is accurate? (There may be more than onecorrect choice.)A) The kinetic energy of the neutron is equal to the energy of the photon.B) The kinetic energy of the neutron is greater than the energy of the photon.C) The neutron and photon have the same momentum.D) The neutron and photon have the same speed.E) None of the above statements are correct.

36)

37) A nonrelativistic electron and a nonrelativistic proton have the same de Broglie wavelength.Which of the following statements about these particles are accurate? (There may be more thanone correct choice.)A) The electron has more momentum than the proton.B) Both particles have the same kinetic energy.C) The electron has more kinetic energy than the proton.D) Both particles have the same speed.E) Both particles have the same momentum.

37)

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

38) Calculate the energy in eV of a neutron (mass 1.675 ! 10-27 kg) that has de Broglie

wavelength of 4.1 ! 10-12 m

(Note: h = 6.626 ! 10-34 J ∙ s, c = 3.00 ! 108 m/s, and e = 1.602 ! 10-19 C.)

38)

39) An unstable particle produced in a high-energy collision is measured to have an energyof 483 MeV and an uncertainty in energy of 84 KeV. Use the Heisenberg uncertaintyprinciple to estimate the lifetime of this particle.

(Note: h = 6.626 ! 10-34 J ∙ s, c = 3.00 ! 108 m/s, and e = 1.602 ! 10-19 C.)

39)

40) A small dust particle m = 7.90 ! 10-6 g is being observed under a magnifying lens. Itsposition is determined to be within 0.0050 mm.(a) Find the velocity limit implied by the uncertainty of its position.(b) Assuming the dust particle is moving at this speed, how many years would it takefor the particle to move 1 mm?

40)

41) An electron, bound to a certain atom, has an ionization energy of 9.03 eV. Assuming thatthis energy is due to the size of the atom that contains it, estimate the size of the atom.

(Note: h = 6.626 ! 10-34 J ∙ s and m e = 9.11 ! 10-31 kg.)

41)

42) A beam of electrons, accelerated through a voltage of 19 V, is directed normally at thesurface of a metal. An intensity maximum occurs when the reflected angle ! is 42° withrespect to the incident beam. Find the spacing, d, between the crystal planes.

(Note: h = 6.626 ! 10-34 J ∙ s, m e = 9.11 ! 10-31 kg, and e = 1.602 ! 10-19 C.)

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43) (a) Through what potential difference must you accelerate an electron from rest so thatits kinetic energy is the same as the energy of a photon of visible light of wavelength550.0 nm?(b) For the photon and electron in part (a), what is the ratio of the de Broglie wavelengthof the electron to the wavelength of the photon?

(Note: h = 6.626 × 10-15 J ∙ s = 4.136 × 10-15 eV ∙ s, c = 3.00 × 108 m/s,

e = 1.60 × 10-19 C, melectron = 9.11 × 10-31 kg.)

43)

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