atom, which is the total number of protons and neutrons in its nucleus.

In a nuclear reactor, there are many, many neutrons that can be used in this reaction; approximately 10¹² to 10¹⁴ (10¹² is a million million; 10¹⁴ is a hundred times 10¹²) pass through each square centimeter of target area every second. Not all these will strike the nuclei of sodium atoms. Of those that do, not all will be captured. A mathematical relationship that tells how many atoms of sodium-24 will be created in a cubic centimeter of the target in one second is:

N₂₄ = N₂₃φσt

where N₂₄ is the number of sodium-24 atoms created during each second in a cubic centimeter of the target; N₂₃ is the number of atoms of sodium-23 in a cubic centimeter of the target; φ is the number of neutrons crossing a square centimeter per second (called the neutron flux); t is the time in seconds that the target is in the reactor; and σ is a number that represents the probability that the conversion of sodium-23 to sodium-24 will occur. This last number is called a “cross section” and it is expressed in “barns”. One barn is equal to 10^-24 square centimeter, which is approximately the cross-sectional area of a typical atomic nucleus.

In an activation analysis experiment, the analyst wants to determine the number of target atoms (N₂₃ in the above example). He can measure how long the target was in the nuclear reactor; there are ways of measuring the neutron flux, φ; and the cross section is fixed and generally known for each target nucleus. So, by measuring the number of radioactive atoms created (N₂₄), he can calculate the number of target atoms. See the figure on the next two pages.

Actually, to get the most accurate results, there are certain practical tricks he can use that increase the accuracy. Some of these will become apparent in later sections of this booklet.

The most important of these “tricks” is the use of a “standard” or “comparator”. This comparator is similar in form and composition to the sample to be measured but contains a known quantity of the element to be determined. The steps used for the analysis are simple.

1. Put the sample and comparator together into a reactor and bombard them with neutrons.

2. Remove them and measure the radioactivity produced from the sample.

3. Compare the radioactivity of the sample and the comparator and calculate the amount of the element in the sample as a proportion:

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).

Step 7. Use c/m/gNa and 1.37 MeV gamma rays counted per minute in sample to calculate grams of sodium in sample.

Step 8. Calculate percent sodium in sample.

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