Duke University Medical Physics Program
MP200  Radiation Physics
Fall 2010
Assignment 06
Due 11/05/10
( Show your work for each problem. Partial credits are awarded.)
1. Derive equations 7.8, 7.9 and 7.10 Attix page 127.
i.e.
hν
=
hν
1 + (
hν
m
0
c
2
)(1

cos
φ
)
T
=
hν
(1

cos
φ
)
m
0
c
2
hν
+ (1

cos
φ
)
cot
θ
= (1 +
hν
m
0
c
2
) tan(
φ
2
)
2. What is the maximum energy a
γ
ray can have after being Comp
ton scattered through 180
0
.
3. Calculate the velocity of recoil electrons when light of wavelength
1
μm
is Compton scattered through 90
0
. Hint: Are the electrons
relativistic?
4. Derive the equation for Compton Scattering,
λ
=
λ
0
+
h
m
0
c
(1

cos
θ
)
A narrow beam containing 10
20
photons at 6
MeV
impinge per
pendicularly on a layer of lead 12
mm
thick, having a density of
11
.
3
g.cm

3
. How many interactions of each type ( photoelectric,
Compton, pair, Rayleigh) occur in the lead?
1
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Assuming that each interaction results in one primary photon be
ing removed from the beam, how much energy is removed by each
type of interaction?
5. Calculate for 1
MeV
photons the
K

N
cross section, and derive
the Compton mass attenuation coefficient for copper.
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 Fall '10
 Guna
 Electron, Photon, Light, Compton scattering, Compton wavelength shift

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