where At 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.
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.
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.