Page 566 - Instrumentation Reference Book 3E

548 Measurements employing nuclear techniques

liquid which has soaked through the leak into the 3c = 1IpL (23.2)
surrounding earth. If one uses a radioisotope with
a very short half-life (half-life is the time taken for a that is, when the thickness of material is equal to
particular radioisotope to decay to half its initial the reciprocal of the linear absorption coeflicient.
activity) the pipeline will be free of radioactive This reciprocal is also called the mean-jiree path,
contamination in a short time, allowing repairs to and it can be shown that for any thickness of a
be carried out without hazard to the workmen particular substance there is an optimum type
repairing it or to the domestic consumer when the and intensity of radioactive source. For very
liquid is, for example, the local water supply. dense materials, and for thick specimens, a source
emitting hi h energy radiation will be required.
& -
Therefore Co, which emits gamma rays of 1.33
'
23.1.1 Radioactive measurement relations and 1.17MeV, is frequently used. At the other
end of the scale, for the measurement of very thin
When radiations from radioactive isotopes pass films such as, for example, Melinex, a soft beta or
through any material, they are absorbed accord- alpha particle emitter would be chosen. For meas-
ing to (1) their energy and (2) the density and type urement of thickness it is generally arranged to
of material. This absorption follows in general have two detectors and one source. The radiation
the relationship from the source is allowed to fall on one detector
Z = ZoBexp-(pLx) (23.1) through a standard piece of the material to be
measured, while the other detector measures the
where Zo is the intensity of the incident radiation, radiation from the source which has passed
I the intensity of the radiation after passing through the sample under test. The signal from
through the material. x the thickness of material each of the pair of detectors is generally com-
(cm), p~ the linear absorption coefficient (cm-') bined as two d.c. levels, the difference between
and B the build-up factor. which drives a potentiometer-type pen recorder.
The absorption coefficient is a factor which
relates the energy of the radiation and the density 23.1.2 Optimum time of measurement
type of material, and suitable tables are available The basic statistics of counting were outlined in the
(Hubbell) from which this factor may be obtained previous chapter (section 22.1 .I). We now consider
for the particular conditions of source and mater- how that is applied to particular measurements.
ial under consideration. As the tables are usually Suppose that the number of photons or par-
given in terms of the mass absorption coefficient
(p~) (generally in cm2/g), it is useful to know that ticles detected per second is n and that the measure-
the linear absorption coefficient (p~) (in cm-') ment is required to be made in a time t. The
may be derived by multiplying the inass absorp- number actually recorded in t s will be iit & Jilt,
where Jnt is the standard deviation of the meas-
tion coefficient (p~) (in cm2/g) by the density (p)
of the material (in g/cm3). It must be borne in urement according to Poisson statistics and is a
mind that in a mixture of materials each will have measure of the uncertainty of the true value of 71t.
a different absorption coefficient for the same The relative uncertainty (coefficient of variation)
radiation passing through the mixture. is given by
The build-up factor, B, is necessary when deal- J(nt)l(nt) = I/J(nt)
ing with gamma- or X-radiation, where scattering
of the incident radiation can make the intensity of A radioisotope instrument is used to measure
the radiation which actually falls on the detector some quality X of a material in terms of the out-
different from what it would be if no scattering put I of a radiation detector. The instrument
were to take place. For electrons or beta particles sensitivity, or relative sensitivity, S, is defined as
this factor can be taken equal to 1. The complica- the ratio of the fractional change SIII in detector
tion of gamma ray absorption is illustrated by the output which results from a given fractional
non-linearity of the curves in Figure 23.1. which change SXIX in the quality being measured, i.e.,
gives the thickness of different materials needed
to effect a ten-fold attenuation in a narrow beam. (23.3)
From equation (23.1) we can obtain some very
useful information in deciding on the optimum If in a measurement, the only source of error is
conditions for making a measurement on a par- the statistical variation in the number of recorded
ticular material, or, conversely, if we have a parti- events, the coefficient of variation in the value of
cular radioactive source, we can determine what the quality measures
are its limits for measuring different materials.
First, it can be shown that the maximum sensi- (23.4)
tivity for a density measurement is obtained when