Download Physics 107 Exam #1 September 12, 1994 Your name: Multiple

Physics 107
Exam #1
September 12, 1994
Your name:
Useful constants (multiple choice problems use the values given here):
neutron mass=1.675x10-27 kg=939.6 MeV/c2 electron mass=9.11x10-31 kg=0.511 MeV/c2
proton mass=1.672x10-27 kg=938.3 MeV/c2 hydrogen mass=1.673x10-27 kg=938.6 MeV/c2
h=6.63x10-34 Js=4.14x10-15 eVs
c=3x108 m/s
g=9.8 m/s2
1 J=6.24x1018 eV
1 eV=1.60x10-19 J
G=6.67x10-11 Nm2/kg2
Multiple Choice. 9 questions, 3 points each, 27 points total.
1. The experiment of Davisson and Germer was important because it demonstrated (a) particle
diffraction, (b) x-ray diffraction, (c) the formation of a single crystal out of a polycrystalline sample
of nickel, (d) that diffraction maxima occur when waves are incident on periodic structures.
2. All magnetic phenomena can be interpreted on the basis of
, charge invariance, and special
relativity. (a) Coulomb's law, (b) Ohm's law, (c) Lorentz contraction, (d) Einstein's principle of
equivalence.
3. In order to observe the wave properties of a particle, the particle's de Broglie wavelength must be
(a) comparable to a typical photon wavelength, (b) comparable to the dimensions of something the
particle interacts with, (c) much greater than the dimensions of something the particle interacts
with, (d) much less than the dimensions of something the particle interacts with.
4. An event horizon is (a) the apparent position of a star whose light has been deflected by the sun,
(b) the surface of a sphere around a black hole whose radius is the Schwarzschild radius, (c) the
surface of charged metal sphere illuminated by photons, (d) the region around a black hole where
electromagnetic forces warp space and time.
5. The density of a moving object is
less than, (b) the same as, (c) more than.
it appears to an observer when the object is at rest. (a)
6. Planck's analysis of blackbody radiation showed that (a) higher-frequency photons are bluer, (b)
electrons have wave properties, (c) the energies of photoelectrons are quantized, (d)
electromagnetic radiation is emitted in separate bursts of energy called "quanta".
7. A photon falling in a gravitational field becomes (a) faster, (b) slower, (c) redder, (d) bluer.
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8. Which of the following is a consequence of the wave properties of an electron? (a) the
photoelectric effect, (b) the magnetic force between moving electrons, (c) electron diffraction by a
crystal, (d) blackbody radiation.
9. According to special relativity, (a) momentum is not conserved in a collision for which the
velocities of the colliding particles are close to the speed of light, (b) energy is liberated in
collisions between particles moving with velocities close to the speed of light, (c) the total energy of
a body never exceeds its rest energy, (d) the separate principles of conservation of mass and energy
are properly stated as the conservation of mass-energy.
Multiple Choice Short Problems. 8 problems, 6 points each, 48 points total.
1. Find the change in frequency of a photon of red light whose original frequency was 7.3x1014 Hz
when it falls through 100 m just above the surface of the earth. (a) 4.80x10 -19 Hz, (b) 15.25x1014
Hz, (c) 1.80 Hz, (d) 7.95 Hz.
2. A meter stick appears only 60 cm long to an observer. How long does it take to pass the
observer? (a) 3.16x10-9 s, (b) 2.5x10-9 s, (c) 1.93x10-9 s, (d) 1.5x10-9 s.
3. A typical interatomic spacing in solids is 2 angstroms, where an angstrom is a unit of length
equal to 10-10 m. Calculate the speed of a proton having a de Broglie wavelength equal to this
typical spacing. A nonrelativistic calculation will suffice. (a) 5.04x10-4 m/s, (b) 198 m/s, (c)
1.98x103 m/s, (d) 1.24x1022 m/s.
4. How many joules of energy per kilogram of rest mass are needed to bring a spacecraft from rest
to a speed of 0.95c? (a) 9.00x1016 J/kg, (b) 1.17x1017 J/kg, (c) 1.98x1017 J/kg, (d) 2.88x1017 J/kg.
5. If the intensity of moonlight at the surface of the earth is 3x10-4 W/m2 and the wavelength of
moonlight is taken to be =550 nm, how many photons from the moon strike a square meter of the
earth's surface every second? (a) 3.62x10-19, (b) 1.33x10-4, (c) 8.30x1014, (d) 2.77x1018.
6. The earth's mass is 5.98x1024 kg and its radius is 6.38x106 m. What would the earth's radius
have to be to prevent photons from escaping from the earth's surface? (a) 8.86x10-3 m, (b) 2.96x103
m, (c) 2.66x106 m, (d) 1.30x109 m.
7. Find the mass of an electron whose velocity is 0.95c. (a) 2.92x10-30 kg, (b) 4.07x10-30 kg, (c)
9.34x10-30 kg, 2.85x10-31 kg.
8. An electron has a wavelength of 7x10-11 m. Its group velocity is (a) 9.62x10-8 m/s, (b) 1.04x107
m/s, (c) 1.65x106 m/s, (d) 0.021 m/s.
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Problems. Three problems, 45 points total. Show all of your work on
separate pages. Answers without work shown receive no credit.
The work function of silver is 4.7 eV. Suppose 1.5 mW of 200-nm light is directed at a
photoelectric cell made of silver. (12 points) If 1 percent of the incident photons produce
photoelectrons, find the current in the cell. (3 points) What is the current if the wavelength of the
light is increased to 300 nm?
Calculate the speed, kinetic energy in MeV, and wavelength of an electron whose mass is triple its
rest mass. (5 points for each part.)
(12 points) Use a nonrelativistic calculation to find the kinetic energy in eV of an electron whose de
Broglie wavelength is the same as that of a 120-keV x-ray. Is the error introduced by the
nonrelativistic calculation significant? (3 points) Justify your answer by comparing the electron's
energy with its rest energy.
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