APPENDIX
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 = Nφσ (1 - e-λt)
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]/t½,(in hours); t½, 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.)