The selling rate of a radioactive isotope is determined by its activity. What will be the second-hand rate of a one month old ³² P ( t_ 1/2 = 14.3 days ) source if it was initially purchased for 800 rupees? (Assume 1 month = 30 days )

Step-by-step solution

The selling rate of the radioactive isotope is directly proportional to its activity. The activity of a radioactive sample after time t is given by A = A₀ ( 1 2 )^ t t_ 1/2 . Since the price is proportional to the activity, the new price P after time t is P = P₀ ( 1 2 )^ t t_ 1/2 . Given P₀ = 800 rupees , t = 30 days , and t_ 1/2 = 14.3 days . Substituting the values: P = 800 ( 1 2 )^ 30 14.3 P = 800 ( 1 2 )^ 2.098 P = 800 2^ 2.098 800 4.28 187 rupees .