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.)
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