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The radioactivity of milk in one sample was 1750 Bq/L due to iodine-131 with half-life 8.04 days. For comparison, find the activity of milk due to potassium. Assume that one liter of milk contains 1.60 g of potassium, of which 0.0117% is the isotope 40K with half-life 1.28X109 yr.
R = [(ln 2)/T][N/A]
where N = Avogadro number [/kmol], A[kg/kmol] is the mass number, ln 2 = 0.693, and T is the half-life in seconds.
One kilogram of a pure radioactive isotope with half-life T[sec] has activity R[Bq/kg]
The unit of activity is Becquerel (1 Bq = 1 decay/sec)
T = (1.28 x 109 yr)( 31,557,600 s/y) = 4.039 x 1016 s
R = [0.693/4.039 x 1016][ 6.0221415 x 1026 / 40] = 2.583 x 108 Bq/kg
R = [2.583 x 108 Bq/kg][0.00160 * 0.0117/100 kg/L] = 48.35 Bq/L