  Calculation of arsenic concentration with no standard for comparison. 1. Determination of arsenic-76 activity produced from 1 microgram of arsenic at the time it comes out of the reactor. We use the equation from page 12: A0 = Nfs (1 - e-?t) where N is the number of target atoms. (One microgram of arsenic contains (10-6 gram/75 grams per mole f is the neutron flux. (This would be known to the reactor operator. It is usually measured by inserting materials of known composition and measuring their activation. In this case, f = 10¹³ neutrons per square centimeter per second.) s is the activation cross section. (Neutron cross sections have been measured and tabulated by scientists. For the activation of arsenic-75 to arsenic-76, the cross section is known to be 4.2 × 10-24 square centimeter.) ? is the disintegration constant for arsenic-76. (Here, ? = (ln 2 t is the time of the irradiation. (Here t is 12 hours.) Therefore: A0, the activity of arsenic-76,
2. Determination of activity of arsenic measured in the sample and corrected back to the time of removal from the reactor. We use the equation: A1 =
where R is the measured count rate. (In this case, R is the number of counts per second observed in the 0.559-MeV gamma-ray peak, which is 5300 counts in 20 minutes or 4.4 counts per second.) 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.) ? 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, =
= 1200 disintegrations per second 3. Calculation of arsenic concentration in the sample. We use the equation: Concentration in parts per million =
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
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