Biomedical Engineering Reference
In-Depth Information
Recoil
electron
Incident
photo
φ
θ
λ
i
Scattered
photon
λ
f
Figure 8.4
Collision of photons with electrons. If the collision energy is higher than ionization en-
ergy, then electrons are ejected from the orbit.
exist. The scattering of photons from charged particles is called Compton scatter-
ing, named after American physicist Arthur H. Compton, who first observed the
scattering of X-rays from electrons in a carbon target and found scattered X-rays
with a longer wavelength than those incident upon the target. Compton explained
and modeled the scattering by assuming a photon and applying conservation of
energy and conservation of momentum principles to the collision between the pho-
ton and the electron. In a Compton scattering interaction, only a partial amount
of the photon's energy is transferred to an electron, and the photon continues to
travel, but at an angle with respect to its initial direction. Compton scattering is of
a slightly lower energy level but still enough to travel through tissue. The energy
shift depends on the angle of scattering and not on the nature of the scattering me-
dium. The shift of the wavelength increases with scattering angle according to the
Compton formula:
h
mV
(
)
λλ λ
−=Δ=
1cos
−
θ
(8.12)
f
i
e
light
λ
f
is the wavelength of the
scattered X-ray photon,
m
e
is the mass of an electron at rest, and
where
λ
i
is the wavelength of incident X-ray photon,
θ
is the scattering
angle of the scattered photon.
EXAMPLE 8.4
An EM wave with a wavelength of 5
×
10
−
12
m hits an electron at rest and the Compton
scatter is observed at 45°
to the incident angle. Calculate the wavelength of the scattered
photon and the energy associated with it.
Solution:
