E is the efficiency of the detector. (In this case, it is the number of counts observed in the 0.559 peak for each 0.559-MeV gamma ray emitted by a radioactive material at the sample distance. This is known for the detector being used by making other measurements and, for the set-up used here, is 0.010.) F is the average number of 0.559-MeV gamma rays emitted in each disintegration of arsenic-76. (This can be deduced from the decay scheme of arsenic-76. See the decay scheme for manganese-56 on page 13. In the decay of arsenic-76 the number of 0.559-MeV gamma rays emitted per disintegration is approximately 0.41.) λ is the disintegration constant for arsenic-76. (0.026, see page 49.) t is the decay time. (This is the number of hours from the time the sample was removed from the reactor to the time it was counted, or 5 hours.) Therefore, A₁, the activity of arsenic-76 produced in the sample at the time of removal from the reactor, = (4.4 counts per second)/(0.010 × 0.41) e^{0.026 × 5 hours} = 1200 disintegrations per second 3. Calculation of arsenic concentration in the sample. We use the equation: Concentration in parts per million = (A₁)/(A₀ × W) 10⁶ where A₁ and A₀ were determined above and W is the weight of sample analyzed or 300 micrograms (0.0003 gram). Therefore the concentration is (1200)/(9 × 10⁴ × 300) × 10⁶ = 44 parts per million. FOOTNOTES [1]There are exceptions. For a few elements there are no stable nuclei. In some cases, there are other differences that make certain atoms radioactive. [2]These gamma rays (called prompt gamma rays because they are instantaneously produced when the neutron is captured) can also be used for analysis and sometimes are, but we will not be discussing this type of analysis in this booklet. [3]Sensitivity in this case means how small an amount of an unknown element can be detected. [4]Nuclide is a general term applicable to all atomic forms of elements. Whereas isotopes are the various forms of a single element (hence are a family of nuclides) and all have the same atomic number and number of protons, nuclides comprise all the isotopic forms of all the elements. [5]The half-life of a radioactive nuclide is the time it takes for half the nuclei in a large sample to undergo decay. Note that after half of them are gone, a second half-life period will reduce the _remainder_ by one half, leaving one quarter of the original number. [6]The disintegration constant is related to the half-life, T_{½}, by the expression: λ = natural logarithm of 2/half-life, or λ = (ln 2)/(T_{½}) = (0.693)/(T_{½}) [7]The detector efficiency is the ratio of the number of gamma rays detected to the number emitted by the sample. [8]A deuteron is the nucleus of a heavy hydrogen (deuterium) atom and consists of one neutron and one proton.