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 × 10⁹per second?

Answer 1

According to the question, when the β⁺ decays to half of its original amount, the emission rate of γ-rays will drop to half. For this, the sample will take 270 days.

Therefore, the required time is 270 days.