University of Colorado, Department of Physics
PHYS3220, Fall 09, HW#2
due Wed, Sep 2, 2PM at start of class
1. Using the formula for fourmomentum conservation (special relativity) to derive the depen
dence of the wavelength of the scattered radiation on the scattering angle in the Compton
eﬀect. How would you interpret the scattering contribution, which appears at the wave
length of the incident radiation at all scattering angles? (10 pts)
2. Derive the Bragg relation for the maxima in the scattering of monochromatic waves (wave
length
λ
) at a chrystal: sin(Θ
max
) =
nλ/
2
d
with
n
= 1
,
2
,
3
,
, and
d
is the lattice spacing.
Assume that the wave penetrates up to the second plane of the lattice only. (10 pts)
3. Calculate the deBroglie wavelength for
a) a neutron with thermal energy
E
kin
= 1/40 eV,
b) an electron with kinetic energies of
E
kin
= 10 eV, 1 keV, 1 MeV,
c) a proton in the particle accelerator at CERN (
E
kin
= 270 GeV),
d) a C
60
molecule with kinetic energy
E
kin
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 Fall '08
 STEVEPOLLOCK
 Particle Physics, Electron, Energy, Momentum, Special Relativity, Radiation, Fundamental physics concepts, kinetic energy Ekin

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