Biomedical Engineering Reference
In-Depth Information
radiation (i.e., of photons) - and, also, deflection of the electron.
Figure 4.8 schematically depicts this process. The law of conserva-
tion of energy implies (ignoring the small amount of energy taken
up by the recoiling nucleus) that
E
′
+
E
′
=
E
electron
photon
electron
E
E
′
where
is the energy of the incident electron,
is the
electron
electron
E
′
energy of the ongoing electron, and
is the energy of the emitted
photon. Both the electron and the photon tend to go off in the near-
forward direction; the higher the energy, the more forward the
trajectory. The energy released in the bremsstrahlung process is
proportional to the first power of the atomic number, Z, of the atom.
There is a curious aspect of the bremmstrahlung process, namely that
detailed calculations of the effect predict the emission of an infinite
number of photons! Physicists hate infinite values, and this was quite
a puzzle when it was first realized. However, the solution was fairly
soon forthcoming. It transpires
that, while there are indeed an
infinite number of photons
photon
emitted, most tend to carry off
an infinitesimal amount of
energy. As a result, the net
energy carried off by all
photons in any fixed range of
energies, down even to zero, is
finite - so, in this manner, the
infinite problem is resolved.
In addition, the net energy
carried off by the photons in
any fixed range of energies is
more or less constant as a
function of the photon energy.
This is shown schematically in
Figure 4.9.
Figure 4.9. Schematic representa-
tion of the photons resulting from
bremsstrahlung of an electron beam
. At low photon
of energy
E
energies, a near-infinite number of
photons are produced (
dashed line
),
but the energy emitted per unit
energy is virtually constant with
photon energy (
blue line
).
electron
While bremsstrahlung is an important effect in many applications
(e.g., in the targets of X-ray tubes and linacs used in radiation
therapy), it is not a substantial factor in the interactions of radiation
with tissue, as we will discuss below.
