Midterm Examination
November 5, 2007
Physics 115A, Fall 2007
E. Abers
Midterm Examination
Solutions and Comments
Name
1.
2.
3.
4.
Total
You may find some of the following useful:
integraldisplay
∞
∞
e

ax
2
dx
=
radicalbigg
π
a
integraldisplay
∞
∞
x
2
e

ax
dx
=
1
2
radicalbigg
π
a
3
integraldisplay
∞
0
x
n
e

x
dx
=
n
!
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2
Midterm Examination
Question 1
[20 Points]
A photon with angular frequency
ω
strikes a free electron at rest. The electron absorbs
the photon, and acquires some speed
v
. Is this process possible? If so, what is the speed of
the final electron? If not, show mathematically why not?
SOLUTION
Suppose the final electron has momentum
p
and energy
E
=
radicalbig
p
2
c
2
+
m
2
c
4
. The initial
photon has energy
planckover2pi1
ω
and momentum
q
where

q

=
planckover2pi1
ω/c
. Energy conservation requires
planckover2pi1
ω
+
mc
2
=
E
and momentum conservation requires
q
=
p
These are not independent! We also need
E
2
=
p
2
c
2
+
m
2
c
4
Therefore
pc
+
mc
2
=
radicalbig
p
2
c
2
+
m
2
c
4
or
p
2
c
2
+ 2
mpc
3
+
m
2
c
4
=
p
2
c
2
+
m
2
c
4
and
q
=
p
= 0, which is incorrect.
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 Fall '08
 Abers
 Physics, Electron, Photon, Light, Midterm Examination

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