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: (Radioactivity in sample)/(Radioactivity in comparator) = (Quantity of element in sample)/(Quantity of element in comparator) Neutron Activation Analysis: Detecting Sodium in a Sample of Plastic Step 1. Weigh a sample and a standard in quartz tubes. [Illustration: Piece of plastic; Standard = sodium carbonate] Step 2. Seal tubes in package for reactor irradiation. [Illustration: Sealed aluminium can; Sealed quartz tubes; Sample; Standard] Step 3. Bombard with neutrons for about 3 hours in a reactor. [Illustration: Neutrons]