Question

57Co decays to 57Fe by β+- emission. The resulting 57Fe is in its excited state and comes to the ground state by emitting γ-rays. The half-life of β+- decay is 270 days and that of the γ-emissions is 10−8 s. A sample of 57Co gives 5.0 × 109 gamma rays per second. How much time will elapse before the emission rate of gamma rays drops to 2.5 × 109 per second?

Answer 1

Explanation:

• As per the question, when the cobalt isotope decays to Ferrous isotope, there will be an emission of beta isotopes.
• When there is a decay of beta, it reduces to the half, that is, the gamma rays emission rate will reduce to the half.
• The decay of beta has the half-life of 270 days and the half life of gamma emissions is 10−8 s.
• Before emitting the gamma rays rate, its emission drops to $2.5 \times 109$ per second. So, the time required is 270 days.