Neutron Activation Analysis: Detecting Sodium in a Sample of Plastic
Step 1. Weigh a sample and a standard in quartz tubes.
Step 2. Seal tubes in package for reactor irradiation.
Step 3. Bombard with neutrons for about 3 hours in a reactor.
Step 4. Remove sample and standard from tubes and place in separate plastic containers to measure gamma rays.
Step 5. Obtain gamma-ray spectrum for sodium-24 in both sample and standard.
Step 6. Use standard to calculate 1.37 MeV gamma rays counted per minute per gram of sodium (c/m/gNa).
c/m/gNa =
| counts/minute measured in 1.37 peak (shaded area above) |
| grams of sodium known to be in standard (step 1.) |
Step 7. Use c/m/gNa and 1.37 MeV gamma rays counted per minute in sample to calculate grams of sodium in sample.
grams Na in sample =
| counts/minute measured in sample |
| c/m/gNa (step 6.) |
Step 8. Calculate percent sodium in sample.
% sodium =
| grams sodium in sample (step 7.) |
| weight of sample (step 1.) |
THE SENSITIVITY[3] OF NEUTRON ACTIVATION ANALYSIS
There are several factors that determine the sensitivity of the method. Some are variable within limits and some, like the cross section, are fixed. Time is variable to a degree, partially determined by the half-life of the nuclide created and with an upper practical limit determined by how long we want to wait for an analysis.
The crucial step in the analytical procedure is the measurement of the number of radioactive atoms that were created.
1. How do we measure how many radioactive atoms are present?
2. Since there will usually be a mixture of elements in a target, and many of these will be made radioactive, how can we tell one from another?
3. Since radioactive atoms are constantly “disappearing” by radioactive decay, how do we obtain the number of atoms created from a measurement made some time after the bombardment has taken place? And what of those atoms disintegrating while others are still being created in the reactor?
Radioactive atoms almost always decay by emitting negatively charged beta particles usually accompanied by gamma rays. Instruments can detect these kinds of radiation, and it is by measuring the radiation that we determine how many radioactive atoms are present. To do this we have to know the types of radiation emitted by the radioactive atoms we are trying to measure. Fortunately each kind of radioactive atom decays with a unique “pattern” scientists call a “decay scheme”. The [figure on the next page] shows a simplified decay scheme for manganese-56, which is produced by activation of manganese, and a diagram showing what the decay scheme means.
Until a few years ago, it was difficult to measure the number of gamma rays of a particular energy that were being emitted by a mixture of radioactive isotopes unless there were only a few such gamma rays with very different energies. Today instruments are available that can really pick them out of a complex mixture. Thus it is usually possible to “separate” with electronic instruments the radioactive element we are interested in measuring. Some of the examples below will show how this might be accomplished.
Each radioactive nuclide[4] also has a characteristic half-life,[5] which is a measure of how fast the radioactive atoms change (transmute) to atoms of another element. In a reactor, even while they are being produced in the target, atoms of the radioactive nuclide are decaying with the particular half-life of the nuclide. The mathematical laws that govern this process tell us that the number of atoms determines the amount of decay; i.e., the more atoms there are, the greater the amount of decay in a given period of time. (The fraction that decays in that time is constant.) As a result, the target eventually becomes “saturated”, that is, the rate of production equals the rate of decay. When the irradiation is first begun, the number of radioactive atoms increases steadily. But eventually, this rate of increase slows down until, at saturation, further irradiation no longer increases the number of radioactive atoms present in the target.
An energy level diagram. The slanted arrows indicate radioactive decay by beta-particle emission. In each case, manganese-56 decays to a certain energy level of iron-56. On the right the energy of each level is indicated. Following a beta emission to a high-energy (excited) state in iron-56, one or more gamma rays are emitted until the nucleus is de-excited to the level marked zero. The vertical arrows indicate gamma rays emitted during the de-excitation process. The energy of each gamma ray is the difference between the levels involved in the change. The numbers above the vertical arrows indicate the relative proportions of gamma rays of different energies emitted from that level.
The mathematical relationship that describes the irradiation process exactly is:
A₀ = Nφσ (1 - e-λt)
where A₀ is the radioactivity produced (disintegrations per cubic centimeter per second); N is the number of target atoms per cubic centimeter in the sample; φ is the neutron flux (neutrons per square centimeter per second); σ is the cross section for the reaction (square centimeters); λ is the disintegration constant[6] for the radioactive atoms produced (number per second); the number “e” is the base of natural logarithms; and t is the irradiation time in seconds. Note that for short irradiation times (t very small), 1-e-λt approximates λt, while for long irradiations (t very large), 1-e-λt approximates 1.
This summarizes what the decay scheme or energy level diagram shows in terms of the relative amounts of betas and gammas emitted in the decay of manganese-56. Thus, you could observe more than three times as many gamma rays having an energy of 0.847 MeV than of 1.811 MeV, etc. Note that while one, and only one, beta is emitted in the decay of one atom of manganese-56, two gammas can sometimes be emitted in one decay.
Of course, when the target is removed from the reactor, the number of radioactive atoms begins to decrease according to the characteristic half-life of the nuclide. The mathematical expression that describes the process of radioactive decay of a single nuclide is:
At = A₀e-λt
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.
* 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)