Biomedical Engineering Reference
In-Depth Information
Thus, the saturation current gives a direct measure of the rate of energy absorption
in the gas. The relationship (10.3) holds independently of any particular condition
on beam geometry, and is therefore of great practical utility. Fortunately, it is the
energy absorbed in a biological system that is relevant for dosimetry; the radiation
intensity itself is usually of secondary importance.
Example
Good electrometers measure currents as small as 10
-16
A. What is the corresponding
rate of energy absorption in a parallel-plate ionization chamber containing a gas for
which
W
=
30 eV per ion pair (eV ip
-1
)?
Solution
From Appendix B, 1 A
1Cs
-1
. Equation (10.3) gives
=
(10
-16
Cs
-1
)
×
30 eV
1.6
E
abs
=
10
4
eVs
-1
.
=
1.88
×
(10.4)
×
10
-19
C
Ionization measurements are very sensitive. This average current would be produced,
for example, by a single 18.8-keV beta particle stopping in the chamber per second.
W
Values
Figure 10.2 shows
W
values for protons (H), alpha particles (He), and carbon and
nitrogen ions of various energies in nitrogen gas, N
2
. The values represent the
average energy expended per ion pair when a particle of initial energy
E
and all of
the secondary electrons it produces stop in the gas. The value for electrons,
W
β
=
34.6
eV ip
-1
, shown by the horizontal line, is about the same as that for protons at
energies
E
>10
keV.
W
values for heavy ions, which are constant at high energies,
increase with decreasing energy because a larger fraction of energy loss results in
excitation rather than ionization of the gas. Elastic scattering of the ions by nuclei
also causes a large increase at low energies.
The data in Fig. 10.2 indicate that
W
values for a given type of charged parti-
cle are approximately independent of its initial energy, unless that energy is small.
This fact is of great practical significance, since it often enables absorbed energy to
be inferred from measurement of the charge collected, independently of the iden-
tity or energy spectrum of the incident particles. Alternatively, the rate of energy
absorption can be inferred from measurement of the current.
W
values for many polyatomic gases are in the range 25-35 eV ip
-1
. Table 10.1
gives some values for alpha and beta particles in a number of gases.
We have defined
W
as the average energy needed to produce an ion pair and
expressed it in eV ip
-1
.Since1eV=
10
-19
J and the charge separated per
1.60
×
ion pair is 1.60
10
-19
C, it follows that
W
has the same numerical value when
expressed either in eV ip
-1
or J C
-1
(Problem 13).
×
