Biomedical Engineering Reference
In-Depth Information
Fig. 8.4
Diagram illustrating Compton scattering of photon
(energy
h
ν
, momentum
h
ν
/
c
) from electron, initially free and
at rest with total energy
mc
2
. As a result of the collision, the
photon is scattered at an angle
θ
with reduced energy
h
ν
and
momentum
h
ν
/
c
, and the electron recoils at angle
ϕ
with total
energy
E
and momentum
P
.
and
h
ν
c
P
sin
sin
θ
=
ϕ
.
(8.11)
Eliminating
P
and
ϕ
from these three equations and solving for
ν
, one finds that
(Problem 12)
ν
1+(
h
ν/
mc
2
)(1 -
cos
θ
)
.
h
h
ν
=
(8.12)
With this result, the Compton shift is given by
c
1
ν
-
1
ν
h
mc
(1 -
cos
θ
λ = λ
-
(8.13)
λ =
=
).
Thus, as Compton found experimentally, the shift does not depend on the incident
photon frequency ν. The magnitude of the shift at
θ
=
90
◦
is
10
-34
h
mc
=
6.63
×
10
8
= 2.43 × 10
-12
m
,
λ =
(8.14)
9.11
×
10
-31
×
3.00
×
