30) A photocathode whose work function is 2.9 eV is illuminated with white light that has a
continuous wavelength band from 400 nm to 700 nm. What is the range of the wavelength band
in this white light illumination for which photoelectrons are not produced?(c = 3.00 × 108 m/s, h
= 6.626 × 10-34 J ∙ s, 1 eV = 1.60 × 10-19 J)
A) 430 nm to 700 nm
B) 400 nm to 480 nm
C) 430 nm to 480 nm
D) 400 nm to 430 nm
E) 480 nm to 700 nm
31) A photocathode that has a work function of 2.4 eV is illuminated with monochromatic light
having photon energy 3.5 eV. What is the wavelength of this light? (c = 3.00 × 108 m/s, h =
6.626 × 10-34 J ∙ s, 1 eV = 1.60 × 10-19 J)
A) 350 nm
B) 330 nm
C) 300 nm
D) 380 nm
E) 410 nm
32) A photocathode having a work function of 2.4 eV is illuminated with monochromatic light
whose photon energy is 3.4 eV. What is maximum kinetic energy of the photoelectrons
produced?(c = 3.00 × 108 m/s, h = 6.626 × 10-34 J ∙ s, 1 eV = 1.60 × 10-19 J)
A) 1.6 × 10-19 J
B) 3.8 × 10-19 J
C) 4.4 × 10-19 J
D) 4.9 × 10-19 J
E) 5.4 × 10-19 J
33) A photocathode having a work function of 2.8 eV is illuminated with monochromatic
electromagnetic radiation whose photon energy is 4.0 eV. What is the threshold (cutoff)
frequency for photoelectron production? (1 eV = 1.60 × 10-19 J, h = 6.626 × 10-34 J ∙ s)
A) 6.8 × 1014 Hz
B) 2.9 × 1014 Hz
C) 7.7 × 1014 Hz
D) 8.6 × 1014 Hz
E) 9.7 × 1014 Hz
34) When it is struck by 240-nm photons, a material having a work function of 2.60 eV emits
electrons. What is the maximum kinetic energy of the emitted electrons? (c = 3.00 × 108 m/s, h
= 6.626 × 10-34 J ∙ s, 1 eV = 1.60 × 10-19 J)
A) 2.58 eV
B) 5.18 eV
C) 2.00 eV
D) 4.21 eV
35) When a photoelectric surface is illuminated with light of wavelength 437 nm, the stopping
potential is measured to be 1.67 V. (1 eV = 1.60 × 10-19 J, e = 1.60 × 10-19 C, melectron = 9.11
× 10-31 kg, h = 6.626 × 10-34 J ∙ s)
(a) What is the work function of the metal, in eV?
(b) What is the maximum speed of the ejected electrons?
36) In her physics laboratory, Mathilda shines electromagnetic radiation on a material and
collects photoelectric data to determine Planck’s constant. She measures a stopping potential of
5.82 V for radiation of wavelength 100 nm, and 17.99 V for radiation of wavelength 50.0 nm. (1
eV = 1.60 × 10-19 J, c = 3.00 × 108 m/s)
(a) Using Mathilda’s data, what value does she determine for Planck’s constant?
(b) What is the work function of the material Mathilda is using, in electron-volts?
37) For a certain metal, light of frequency 7.24 × 10-14 Hz is just barely able to dislodge
photoelectrons from the metal. (h = 6.626 × 10–34 J ∙ s, 1 eV = 1.60 × 10-19 J, e = 1.60 × 10-19
C)
(a) What will be the stopping potential if light of frequency 8.75 × 10-14 Hz is shone on the
metal?
(b) What is the work function (in electron-volts) of this metal?
38) When light of wavelength 350 nm is incident on a metal surface, the stopping potential of the
photoelectrons is measured to be 0.500 V. What is the work function of this metal? (c = 3.00 ×
108 m/s, h = 6.626 × 10-34 J ∙ s, 1 eV = 1.60 × 10-19 J)
A) 0.500 eV
B) 3.05 eV
C) 3.54 eV
D) 4.12 eV
39) When light of wavelength 350 nm is incident on a metal surface, the stopping potential of the
photoelectrons is 0.500 V. What is the threshold (cutoff) frequency of this metal? (c = 3.00 ×
108 m/s, h = 6.626 × 10-34 J ∙ s, 1 eV = 1.60 × 10-19 J)
A) 3.47 × 1014 Hz
B) 3.74 × 1014 Hz
C) 4.73 × 1014 Hz
D) 7.36 × 1014 Hz
40) When light of wavelength 350 nm is incident on a metal surface, the stopping potential of the
photoelectrons is 0.500 V. What is the maximum kinetic energy of these electrons? (c = 3.00 ×
108 m/s, h = 6.626 × 10-34 J ∙ s, 1 eV = 1.60 × 10-19 J)
A) 0.500 eV
B) 3.04 eV
C) 3.54 eV
D) 4.12 eV
41) A monochromatic light beam is incident on the surface of a metal having a work function of
2.50 eV. If a 1.0-V stopping potential is required to make the electron current zero, what is the
wavelength of light? (c = 3.00 × 108 m/s, h = 6.626 × 10-34 J ∙ s, 1 eV = 1.60 × 10-19 J)
A) 355 nm
B) 423 nm
C) 497 nm
D) 744 nm
42) Calculate the kinetic energy, in electron-volts, of a neutron that has a de Broglie wavelength
of (mneutron = 1.675 × 10-27 kg, 1 eV = 1.6 × 10-19 J, h = 6.626 × 10-34 J ∙ s)
43) How “slow” must a 200-g ball move to have a de Broglie wavelength of 1.0 mm? (h = 6.626
× 10-34 J ∙ s)
44) What would be the de Broglie wavelength for 1-g object moving at the earth’s escape speed
25,000 mph (about 11 km/s)? (h = 6.626 × 10-34 J ∙ s)
45) Atoms in crystals are typically separated by distances of 0.10 nm. What kinetic energy must
a nonrelativistic electron have, in electron-volts, in order to have a wavelength of 0.10 nm?
(melectron = 9.11 × 10–31 kg, 1 eV = 1.60 × 10–19 J, h = 6.626 × 10-34 J ∙ s)
46) The electrons in a beam are moving at 18 m/s. (melectron = 9.11 × 10-31 kg, h = 6.626 ×
10-34 J ∙ s)
(a) What is its de Broglie wavelength these electrons?
(b) If the electron beam falls normally on a diffraction grating, what would have to be the
spacing between slits in the grating to give a first-order maximum at an angle of 30° with the
normal to the grating?
47) A proton that is moving freely has a wavelength of 0.600 pm. (mproton = 1.67 × 10-27 kg, e
= 1.60 × 10-19 C, h = 6.626 × 10-34 J ∙ s)
(a) What is its momentum?
(b) What is its speed?
(c) What potential difference would it have been accelerated through, starting from rest, to reach
this speed?
48) A crystal diffracts a beam of electrons, like a diffraction grating, as they hit it perpendicular
to its surface. The crystal spacing is 0.18 nm, and the first maximum scattering occurs at 80°
relative to the normal to the surface. (e = 1.60 × 10-19 C, melectron = 9.11 × 10-13 kg, h = 6.626
× 10-34 J ∙ s)
(a) What is the wavelength of the electrons?
(b) What potential difference accelerated the electrons if they started from rest?
49) What is the wavelength of the matter wave associated with a 0.50-kg ball moving at 25 m/s?
(h = 6.626 × 10-34 J ∙ s)
A) 3.5 × 10-35 m
B) 5.3 × 10-35 m
C) 3.5 × 10-33 m
D) 5.3 × 10-33 m
50) What is the de Broglie wavelength of a ball of mass 200 g moving at 30 m/s? (h = 6.626 ×
10-34 J ∙ s)
A) 1.1 × 10-34 m
B) 2.2 × 10-34 m
C) 4.5 × 10-28 m
D) 6.7 × 10-27 m
51) A person of mass 50 kg has a de Broglie wavelength of 4.4 × 10-36 m while jogging. How
fast is she running? (h = 6.626 × 10-34 J ∙ s)
A) 2.0 m/s
B) 3.0 m/s
C) 4.0 m/s
D) 5.0 m/s
52) Find the de Broglie wavelength of a 1.30-kg missile moving at (h = 6.626 × 10-34 J
∙ s)
A) 1.81 × 10-35 m
B) 2.05 × 10-35 m
C) 2.28 × 10-35 m
D) 2.57 × 10-35 m
53) If an electron has a wavelength of 0.123 nm, what is its kinetic energy, in electron-volts?
This energy is not in the relativistic region. (melectron = 9.11 × 10–31 kg, 1 eV = 1.60 × 10-19 J,
h = 6.626 × 10-34 J ∙ s)
A) 19.8 eV
B) 60.2 eV
C) 80.4 eV
D) 99.5 eV
E) 124 eV
54) What is the wavelength of the matter wave associated with an electron moving with a speed
of 2.5 × 107 m/s? (melectron = 9.11 × 10-31 kg, h = 6.626 × 10-34 J ∙ s)
A) 29 pm
B) 35 pm
C) 47 pm
D) 53 pm
55) After an electron has been accelerated through a potential difference of 0.15 kV, what is its
de Broglie wavelength? (e = 1.60 × 10-19 C, melectron = 9.11 × 10-31 kg, h = 6.626 × 10-34 J ∙
s)
A) 0.10 nm
B) 1.0 nm
C) 1.0 mm
D) 1.0 cm
56) If the momentum of an electron is 1.95 × 10–27 kg ∙ m/s, what is its de Broglie wavelength?
(h = 6.626 × 10-34 J ∙ s)
A) 340 nm
B) 210 nm
C) 170 nm
D) 420 nm
E) 520 nm
57) If the de Broglie wavelength of an electron is 380 nm, what is the speed of this electron?
(melectron = 9.11 × 10–31 kg, h = 6.626 × 10-34 J ∙ s)
A) 2.0 km/s
B) 3.8 km/s
C) 1.9 km/s
D) 4.1 km/s
E) 5.2 km/s
58) An electron is moving with the speed of 1780 m/s. What is its de Broglie wavelength?
(melectron = 9.11 × 10–31 kg, h = 6.626 × 10-34 J ∙ s)
A) 409 nm
B) 302 nm
C) 205 nm
D) 420 nm
E) 502 nm
59) If the de Broglie wavelength of an electron is 2.4 μm, what is the speed of the electron?
A) 3.0 × 102 m/s
B) 2.5 × 105 m/s
C) 1.7 × 103 m/s
D) 8.3 × 106 m/s
60) If an electron has the same de Broglie wavelength as the wavelength of a 390-nm photon in
vacuum, what is the speed of the electron? (melectron = 9.11 × 10-31 kg, c = 3.0 × 108 m/s, h =
6.626 × 10-34 J ∙ s)
A) 1900 m/s
B) 2100 m/s
C) 1700m/s
D) 1500 m/s
E) 540 m/s
61) A proton has a speed of 7.2 x m/s. What is the energy of a photon that has the same
wavelength as the de Broglie wavelength of this proton? (melectron = 9.11 × 10-31 kg, c = 3.00
× 108 m/s, h = 6.626 × 10-34 J ∙ s)
A) 230 keV
B) 150 keV
C) 300 keV
D) 370 keV
E) 440 keV
62) An electron has the same de Broglie wavelength as the wavelength of a 1.8 eV photon. What
is the speed of the electron? (melectron = 9.11 × 10-31 kg, c = 3.00 × 108 m/s, 1 eV = 1.60 ×
10-19 J)
A) 1100 m/s
B) 980 m/s
C) 910 m/s
D) 840 m/s
E) 770 m/s
63) An electron is accelerated from rest through a potential difference. After acceleration the
electron has a wavelength of 880 nm. What is the potential difference responsible for the
acceleration of the electron? (h = 6.626 × 10-34 J ∙ s, melectron = 9.11 × 10-31 kg, e = 1.6 10-19
C)
A) 1.9 × 10-6 V
B) 1.7 × 10-6 V
C) 2.2 × 10-6 V
D) 2.5 × 10-6 V
64) Electrons emerge from an electron gun with a speed of 2.0 × 106 m/s and then pass through a
double-slit apparatus. Interference fringes with spacing of 2.7 mm are detected on a screen far
from the double slit. What would the fringe spacing be if the electrons were replaced by neutrons
with the same speed? (h = 6.626 × 10-34 J ∙ s, melectron = 9.11 × 10-31 kg, mneutron = 1.675 ×
10-27 kg)
A) 1.5 μm
B) 4.9 m
C) 0.93 nm
D) 1.2 km
65) Electrons are accelerated to a speed of 4.0 × m/s and are then aimed at a double-slit
apparatus, where interference fringes are detected. If the electrons were replaced by neutrons,
what speed must neutrons have to produce interference fringes with the same fringe spacing as
that observed with the electrons? (h = 6.626 × 10-34 J ∙ s, melectron = 9.11 × 10-31 kg, mneutron
= 1.675 × 10-27 kg)
A) 2.2 × 101 m/s
B) 7.3 × 107 m/s
C) 1.7 × 106 m/s
D) 9.3 × 102 m/s
66) Electrons with a speed of 2.1 × 106 m/s are directed towards a 1.0-μm wide slit. An electron
detector is placed 1.0 m behind the slit. How wide is the central maximum of the electron
diffraction pattern on the detector? (h = 6.626 × 10-34 J ∙ s, melectron = 9.11 × 10-31 kg)
A) 690 μm
B) 350 μm
C) 1000 μm
D) 1400 μm
67) A certain crystal has a spacing of 0.442 nm between atoms. A beam of neutrons moving with
a speed of 1640 m/s perpendicular to the surface is diffracted as it passes through the crystal.
What is the angle from the central maximum to the next interference maximum? (mneutron =
1.675 × 10-27 kg, h = 6.626 × 10-34 J ∙ s)
A) 17.0°
B) 21.0°
C) 33.1°
D) 60.0°
E) 90.0°
68) The spacing of the atoms of a crystal is 159 pm. A monoenergetic beam of neutrons directed
normally at the surface of the crystal undergoes first order diffraction at an angle of 58° from the
normal. What is the energy of each of the neutrons? (mneutron = 1.675 × 10-27 kg, 1 eV = 1.6 ×
10-19 J, h = 6.626 × 10–34 J ∙ s)
A) 0.045 eV
B) 0.039 eV
C) 0.050 eV
D) 0.056 eV
E) 0.061 eV