Biomedical Engineering Reference
In-Depth Information
This equation has only the trivial solution
β
= 0
and
γ = 1
, which, by Eq. (8.6), leads
to the condition
h
ν = 0
. We conclude that the photoelectric effect occurs because
the absorbing electron interacts with the nucleus and the other electrons in the
atom to conserve the total energy and momentum of all interacting partners.
We now turn to the scattering of photons by electrons.
8.4
Compton Effect
Figure 8.2 illustrates the experimental arrangement used by Compton in 1922.
Molybdenum
K
α
X rays (photon energy 17.4 keV, wavelength
λ =
0.714
Å) were
directed at a graphite target and the wavelengths λ
of scattered photons were mea-
sured at various angles
θ
with respect to the incident photon direction. The intensi-
ties of the scattered radiation versus λ
for three values of
θ
are sketched in Fig. 8.3.
Each plot shows peaks at two values of λ
: one at the wavelength λ of the incident
photons and another at a longer wavelength, λ
>
λ. The appearance of scattered
radiation at a longer wavelength is called the Compton effect. The Compton shift
in wavelength,
λ = λ
-
λ
, was found to depend only on
θ
; it is independent of the
incident-photon wavelength
λ
. In the crucial new experiment in 1922, Compton
measured the shift
λ =
90
◦
.
The occurrence of scattered radiation at the same wavelength as that of the inci-
dent radiation can be explained by classical electromagnetic wave theory. The elec-
tric field of an incident wave accelerates atomic electrons back and forth at the same
frequency
ν =
c
/λ
with which it oscillates. The electrons therefore emit radiation
with the same wavelength. This Thomson scattering of radiation from atoms with
no change in wavelength was known before Compton's work. The occurrence of
the scattered radiation at longer wavelengths contradicted classical expectations.
0.024
Åat
θ
=
Fig. 8.2
Compton measured the intensity of scattered photons
as a function of their wavelength
λ
at various scattering
angles
θ
. Incident radiation was molybdenum
K
α
X rays, having
a wavelength
λ =
0.714 Å.
