Question

${}^{57}\text{Co}$ decays to ${}^{57}\text{Fe}$ by ${\beta }^{+}$ emission. The resulting ${}^{57}\text{Fe}$ is in its excited state and comes to the ground state by emitting $\gamma$ rays. The half-life of ${\beta }^{+}$ decay is 270 days and that of the $\gamma$ emission is ${10}^{-6}$ s. A sample of ${}^{57}\text{Co}$ gives 5.0$\times {10}^9$ gamma rays per second. How much time will elapse before the emission rate of gamma rays drops to 2.5 $\times {10}^9$

Answer 1

According to the question, the emission rate of $\gamma$ - rays will drop to the half when the $\beta +$ decays to half of its original amount and for this the sample would take 270 days.

$\therefore$ The required time is 270 days