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Phy 3031 Modern physics, Spring 2007
Homework set #8. Due at the start of class on Wednesday, February 28, 2007.
For numerical answers give two significant digits. The first should be correct, the second can
be approximate.
1. A particular radiating cavity has the maximum of its spectral distribution at a wavelength of 29µm = 29 × 10−6 m. The temperature is then changed so that the total
power radiated by the cavity increases by a factor of 4.
(a) At what wavelength does the new spectral distribution have its maximum?
(b) What is the new temperature of the cavity?
2. Give your answers in units of pm or MeV.
(a) What is the Compton wavelength, h/mc, of an electron?
(b) What is the energy of a photon whose wavelength is equal to the Compton wavelength of an electron?
(c) What is the Compton wavelength of a proton?
(d) What is the energy of a photon whose wavelength is equal to the Compton wavelength of a proton?
3. A gold foil of thickness 2µm is used in a Rutherford scattering experiment to scatter α
particles with energy 7 MeV. For gold, ρ = 19.3 g/cm3 , and M = 197 g/mol. Hint: See
example 4.2 in the textbook and use the numbers calculated there—except the kinetic
energy of the α particle and the thickness of the gold in this problem differ from those
in the textbook example.
(a) What fraction of the particles will be scattered at angles greater than 90◦ ?
(b) What fraction will be scattered at angles between 45◦ and 75◦ ?
4. In Rutherford scattering
(a) What is the distance of closest approach rd to a gold nucleus for an α particle of
5 MeV?
(b) For an α particle of 10 MeV?
(c) For an α particle of 20 MeV?