Question

${}^{57}\text{Co}$ decays to ${}^{57}\text{Fe}\text{by}{\beta }^{+}$ emission. The resulting ${}^{57}\text{Fe}$ is in its excited state and comes to the ground state by emitting $\gamma -\text{rays}$. The half-life of ${\beta }^{+}$ is $270\text{days}$ and that of the $\gamma -$ emission is ${10}^{-8}\text{s}$. 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 $2.5\times {10}^9$ per second?

• A. $540\text{days}$
• B. $135\text{days}$
• C. $270\text{days}$
• D. $108\text{days}$

Answer 1

The correct option is C $270\text{days}$

According to the question, emission rate of $\gamma$ rays will drop to half when the ${\beta }^{+}$ decays to half of its original amount.

And for this, the sample would take $270\text{days}$.

$\therefore$ The required time is $270\text{days}$.

Hence, option $\left(C\right)$ is correct.

Why this question? To make the student aware that do net get confused with the given data, sometimes data are given to deviate the student from basic concepts.