From Radiochemistry and Nuclear Methods of Analysis, by William D. Ehmann and Diane E. Vance:
Ch. 9 # 1.)
A 32.50-mg sample of naturally occurring elemental silicon was irradiated with neutrons in a nuclear reactor at a flux density of 2.75E-13 thermal neutrons per (cm^2 sec). The activity of 31-Si was determined at a remote site with a beta particle detector that has a counting efficiency of 16.5%. Transport of the sample to the remote counting site and chemical processing (RNAA) to isolate a pure Si counting sample required a delay time of 8.00 h prior to counting. The chemical yield of the RNAA procedure was 97.5%. If permitted by the experimental parameters, how long a reactor irradiation would be required to produce the following counting rates at the remote site?
(a) 6.00E5 counts per minute
(b) 9.78E8 counts per minute.
Note: The cross section for the reaction = 107 mb and the half life of Si-31 = 2.62 h. Si-31decays >99.9% of the time to the ground state of P-31 via negatron emission.