where N is the number of target atoms. (One microgram of arsenic
contains (10^{-6} gram/75 grams per mole[12]) × 6.02 × 10²³ atoms per
mole which is 8 × 10¹⁵ atoms of arsenic.)
φ 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, φ = 10¹³ neutrons per square
centimeter per second.)
σ 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.)
λ is the disintegration constant for arsenic-76. (Here, λ = (ln
2[13]/t_{½},(in hours); t_{½}, the half-life for arsenic-76, is 26.6
hours so λ = (0.693/26.6) = 0.026.)
t is the time of the irradiation. (Here t is 12 hours.)
Therefore: A₀, the activity of arsenic-76,
= 8 × 10¹⁵ × 10¹³ × 4.2 × 10^{-24} × (1 - e^{-0.026 × 12})
(Note: e is a physical constant, 2.71+)
= 9 × 10⁴ disintegrations per second per microgram
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: