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MODERN PHYSICS
PHY 320
EXAM 2
(April 5, 2005)
(Answer all questions. To get partial credits show all the steps of your calculation
clearly. Good luck.)
h = 6.626 x 10-34 J.s
1 eV = 1.602 x 10-19 J
me = 9.109 x 10-31 kg = 0.5110 MeV/c2
mp = 1.673 x 10-27 kg = 938.3 MeV/c2.
c = 3.0 x 108 m/s
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1. Briefly and clearly answer the following questions:
(a) Briefly describe Rutherford’s model of the atom. What are the major
drawbacks of his model? Explain your answer briefly. (4+4=8 pts)
(b) The Bohr theory of the hydrogen atom is based on several assumptions.
What are these assumptions? Do any of these assumptions contradict
classical physics? What are some of the drawbacks of Bohr’s model of the
atom?
(4+3+3=10 pts)
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(c) All objects radiate energy. Why then, are we not able to see all objects in
a dark room? (4 pts.)
Ans:
(d) Some stars are observed to be reddish, and some are blue. Which stars
have the higher surface temperature? Explain. (4 pts.)
Ans:
(e) Explain why there are in general two peaks in the X-ray intensity versus
wavelength plot in the Compton scattering experiment. (4 pts.)
Ans:
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Problems: (Points will be taken off for not showing the steps of your
calculation and for not getting the right numbers.)
2. The size of an atom is approximately 10-8 cm. To locate an electron within
the atom, one should use electromagnetic radiation of wavelength not longer
than, say, 10-9 cm. (a) What is the energy of a photon with such a wavelength
(in eV)? (b) What is the uncertainty in the electron’s momentum if we are
certain about its position by 10-9 cm? (5 + 5 =10 pts.)
Ans:
3. The work function for potassium is 2.24eV. If potassium metal is illuminated
with light of wavelength 350 nm, find (a) the maximum kinetic energy of the
photoelectrons and (b) the cutoff wavelength. (8+ 7=15 pts.)
Ans:
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4. The Sun gets its energy from a sequence of nuclear reactions called the
proton-proton cycle. These reactions take place near the Sun’s center and
have the net effect
4p → He + 2e+ + 2ν + 5γ.
The particles involved being (in order) are protons, helium nuclei, positrons,
neutrinos, and high-energy photons (called γ rays). About 95% of the energy
released in this composite reaction goes to the γ ray photons, whose average
wavelength is about 250 fm (1 fm = 10-15 m).
(a) What is the total energy released in the above reaction? The mass of the
neutrino is so small that you can take it to be zero.
(b) Over the course of a few million years, these γ rays diffuse toward the
surface and are slowly converted into visible photons. About how many
visible photons are generated from one of the original γ ‘s? (7+8=15 pts.)
[Visible photons are within 400 – 650 nm]
Ans:
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5. Gamma rays of energy 1.02 MeV are scattered from electrons that are
initially at rest. If the scattering is symmetric, that is θ = ϕ, find (a) the
scattering angle θ and (b) the energy of the scattered photons. (8+7=15pts)
Ans:
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6. (a) For waves on deep water (depth h much greater than wavelength λ) the
wave (phase) velocity is given by vwave = g / k . Prove that for these waves,
the packet (group) velocity vpack is half the wave velocity vwave. (b) In shallow
water (h << λ), vwave =
Ans:
gh . Prove that, in this case, vpack = vwave. (15 pts.)
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