A radioactive element of mass $1 \mathrm{~kg}$ after $N$ years is left with only. $125 \mathrm{~g}$. If the…
A radioactive element of mass $1 \mathrm{~kg}$ after $N$ years is left with only. $125 \mathrm{~g}$. If the half life of the element is $12.5 \mathrm{y}$, then the value of $N$ is
37.5 years
25.0 years
50.0 years
75.0 years
Solution
( ) Given: Initial amount of radioactive substance is $1 \mathrm{~kg}$ and half-life is $12.5 \mathrm{y}$.
Decay scheme will be
$1 \mathrm{~kg} \xrightarrow{125 y} 500 \mathrm{~g} \xrightarrow{125 y} 250 \mathrm{~g} \xrightarrow{125 y} 125 \mathrm{~g}$
So time required is
$t=3 \times T_{1 / 2}=3 \times 12.5=37.5 \text { years }$