Biomedical Engineering Reference
In-Depth Information
Fig. 8.3
Intensity vs. wavelength
λ
of photons scattered at
angles (a)
θ
=
45
◦
,(b)90
◦
, and (c) 135
◦
.
To account for his findings, Compton proposed the following quantum model.
In Fig. 8.4(a), a photon of energy
h
ν
and momentum
h
ν
/
c
(wavy line) is incident
on a stationary, free electron. After the collision, the photon in (b) is scattered at
an angle
θ
with energy
h
ν
/
c
. The struck electron recoils at an
angle
ϕ
with total energy
E
and momentum
P
. Conservation of total energy in
the collision requires that
ν
and momentum
h
+
mc
2
ν
+
E
.
(8.9)
h
ν
=
h
Conservation of the components of momentum in the horizontal and vertical di-
rections gives the two equations
h
ν
c
c
=
h
+
P
cos
ϕ
cos
θ
(8.10)
