where A_{t} is the radioactivity of an isotope at some time, t, after
the end of the irradiation, and A₀ is the radioactivity at the end of
the irradiation.
[Illustration: Fraction of saturation sodium-24 activity _vs_ Time of
irradiation (hours)]
The activation of sodium-23 to sodium-24, which has a half-life of 15
hours. The horizontal line marked 1.0 represents the “saturation”
activity level for a sample of sodium of a certain size in a constant
neutron flux. Note that after about 120 hours, the activity of the
sample is within 1% of the value at saturation, which is the most
active that sample will ever become at a given φ. Note also that after
the first 15 hours (1 half-life) the sample is exactly half way to its
value at saturation. Thus long irradiations are useful to increase the
sensitivity of the analysis, but only up to a certain point.
The result of all this is that the sensitivity of an analysis depends in
practice on a number of practical as well as theoretical factors:
1. The cross section of the target element.
2. The half-life of the radioactive isotope produced.
3. The time available for irradiation.
4. The flux of neutrons available for irradiation.
5. The promptness with which we can begin measuring radioactivity and
the efficiency of this measurement.
6. Possible interferences due to the presence of elements yielding the
same radioactive elements or those yielding very similar
radiations.
In the next section of this booklet, there are several examples that
will show you how all this works in practice. But to summarize what
these factors mean in terms of sensitivity let us look at the chart in
the figure on page 18. Here all the elements are arranged in a periodic
table. The sensitivities are shaded in coded ranges representing
measurable quantities. They are calculated on the basis that there are
no interferences, that the neutron flux is 10¹⁴ neutrons per square
centimeter per second, and that we can measure 100 gamma rays per minute
without much difficulty assuming a gamma-ray detector efficiency[7] of
10%. The elements labeled β yield radioisotopes that emit few or no
gamma rays and can only be analyzed by neutron activation using
appropriate chemical separation procedures followed by beta
radioactivity measurements. Such chemical separation procedures (to
remove unwanted radioactive isotopes of other elements) are also
sometimes useful to improve the sensitivity of the analysis of gamma-ray
emitters if necessary.
[Illustration: Graph: “Fraction of Sodium-24 remaining” vs. “Time of
decay (hours)”]
The radioactive decay curve of sodium-24. The vertical scale is not
_linear_ but _logarithmic_. Thus, each factor of two in radioactivity
occupies the same distance along the vertical axis. When two samples
are being analyzed for sodium by activation analysis, they must be
compared at the same time after they have been removed from the
neutron flux. If this period of time is different, then a correction
must be applied to one of them, based on the decay curve shown here,
to allow for the difference in decay time for the two. Waiting too
long after the irradiation is completed results in much poorer
sensitivity for the analysis depending on the half-life of the
activation product. In this case, after 2 days it takes approximately
ten times as much sodium to yield the same radioactivity as it would
if the sample were measured when it was fresh out of the reactor.
It is not practical to determine a few elements, shown in black squares,
by activation analysis. Some others, like oxygen and nitrogen (labeled
HE), can be measured by using other projectiles like fast (more
energetic) neutrons, or protons or deuterons[8] produced in a device
called an accelerator. Other elements, those shown in white squares, can
be detected with such great sensitivity, that one can find some in
almost everything. For example, if you had a cube of “pure” aluminum
only 1 millimeter on a side, you could detect gold in it if there were
only one atom of gold for every fifty billion atoms of aluminum.
While it isn’t often that you would want to find a gold needle in an
aluminum haystack, the next section presents some practical
applications. Imagine yourself as the person with the problem in these
situations.
[Illustration: Periodic table of elements, with sensitivity code]
* Th and U are radioactive but with such long half-lives that
neutron activation analysis can be used for their determination.
† µg = Microgram (one-millionth of a gram)