Question

Cobalt-57 is radioactive, emitting $\beta $ -particles. The half-life for this is $270$ days. If $100 \, mg$ of this is kept in an open container, then what mass (in $mg$ ) of Cobalt-57 will remain after $540$ days?

Answer 1

Here, $T_{\frac{1}{2}}=270$ days.
After $540$ days, it means two half lives have been completed i.e., $n=2$
If $\frac{N}{N_{0}}=\left(\frac{1}{2}\right)^{n}$
$\Rightarrow \, \, \frac{m}{m_{0}}=\left(\frac{1}{2}\right)^{n} \, $ [ $\because \, \, $ from Equation. (i)]
$\Rightarrow \, \frac{m}{100}=\frac{1}{4}$
$\Rightarrow \, m=25 \, mg$