A portion of the gamma-ray spectrum obtained after neutron activation of a human body. The area in the 3.10-MeV peak, which is above the background due to sodium and chlorine activities, is a measure of the quantity of calcium in the body of the subject. A computer may make the necessary corrections due to the background (which results from overlapping of part of the other gamma-ray peaks). _The Solution_ One reason that ordinary analytical methods are so slow, in this case, is because the amount of copper you are looking for is so small that you would have to dissolve a large amount of plastic to get enough copper to measure. You know that nearly all the plastic is carbon, hydrogen, and oxygen and that none of these elements are easily made radioactive when they are bombarded with low-energy neutrons. You look in a table to see if copper is easily activated. You find that there are two stable isotopes of copper having atomic weights of 63 and 65. Each of these is easily activated, giving radioactive isotopes, copper-64 and copper-66. The latter has a half-life of about 5 minutes and emits gamma rays with energies of 1.039 MeV, which are easy to measure. In the research building next door, there is a small reactor that can irradiate encapsulated samples with low-energy neutrons at the rate of a million million neutrons per square centimeter per second (10¹² neutrons/cm²/sec). You calculate that if you irradiate only one tenth of a gram of the plastic for 10 minutes, and if the plastic contains only one part of copper in one million parts of plastic, then at the end of the irradiation the radioactive copper formed will be emitting over 400 gamma rays per second. There is a pneumatic tube that can remove the irradiated sample in 20 seconds, and you decide that it will take only a minute or two to remove the sample from its capsule and get it into a gamma-ray counter located nearby. The counter is a scintillation counter that is connected to a pulse-height analyzer. If you count for only 10 minutes you will detect about 1000 gamma rays of the right energy (allowing for the inefficiencies of the detector system). This sounds like it should do the job. But does the good plastic contain copper too? And how much does it take to produce the discoloration? You decide to use neutron activation analysis and to analyze samples of faulty plastic, normal plastic, and a small piece of copper foil, which you have weighed and sealed in a small polyethylene bag as a standard. Your results are shown in the table below. Sample Counts in 10 minutes[11] 0.1 grams faulty plastic 100,000 0.1 grams good plastic 1,000 0.1 milligrams of pure copper 1,000,000