Page 142 - Radiochemistry and nuclear chemistry

Absorption of Nuclear Radiation 127

I
Ir
I
Y
i f
d

The activity measured is proportional to the particle flux ~ reaching the detector

R = kde t ~ (6.4)

where kde t = Sde t ~bde t and

t~ = ~abs t~0 (6.5)

and

r = ~bsample nA/(47rr 2 ) (6.6)

$0 is the flux of particles (particles m- 2 S- 1) which reach the detector from the source when
~kabs - 1, and n is the number of particles emitted per decay (n > 1 only for y following
c~- and B-decays). Thus if every B-decay yields 2y (in cascade) and y is the measured
radiation, then n v = 2, and #0 = n~At3/(4r r 2 ) y-quanta m -2 s-1. In branched decay n
will not be an integer. Equation (6.6) is the so called 1/r 2-law since the measured flux
varies as the inverse of the square of the distance to the source.
These equations are valid as long as the conditions at the source and at the detector, as
well as r, are kept constant. When an absorber is inserted between the source and detector
(Fig. 6.1), ~kabs depends on the absorber thickness x (m). For zero absorber thickness, flabs
= 1 in accurate measurements. There is a small absorption due to the air between the
sample and detector unless the measurement is done in a vacuum.
Absorption curves relate the variation of either R or q~ to the thickness of the absorbing
material. In Figure 6.3 the relative transmission ~/~0 is plotted as a function of absorber
thickness for different kinds of radiation. For charged particles, i.e. electrons, protons, and
heavier ions, #/#Q reaches zero at a certain x-value (Xmax); this is referred to as the
maximum range, R, of the particles. The range can be expressed by either the average
range (x = C 1 for heavy ions and C 3 for electrons) or the maximum (or extrapolated) range
(C 2 and C 4, respectively, in Fig. 6.3). The loss of energy involves collisions with atomic
electrons, and the energy loss per collision and the number or collisions varies from one
ionizing particle to the next, resulting in a slight straggling in the range. The average range
is the meaningful one.
Figure 6.4 shows an absorption curve for 32p. The radioactivity R has been measured as
a function of aluminum absorber thickness in linear density, kg m-2 or more commonly mg
cm -2. The low activity "tail" (C 4 in Fig. 6.4) is the background activity R b, which has to
be subtracted from the measured value R m to obtain the true value for the radiation (e.g.
32p). R = R m - R b. The extrapolation of R to a value equal to R b (i.e. C3) gives the range.