Question

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

• A. $50mg$
• B. $\left(\frac{50}{\sqrt{2}}\right)mg$
• C. $25mg$
• D. Zero

Answer 1

The correct option is C $25mg$

Given : $T_{1/2}=270$ days
Time of observation $t=540$ days
So, $n=\frac{t}{T_{1/2}}=\frac{540}{270}=2$
Thus amount of Cobalt-57 remaining $R_{rem}=\frac{R_{initially}}{2^n}$
$\therefore$ $R_{rem}=\frac{100mg}{2^2}=25mg$