A radioactive material whose half life period is 2 years weighs $1 \mathrm{~g}$ and is stored in the…
A radioactive material whose half life period is 2 years weighs $1 \mathrm{~g}$ and is stored in the laboratory for 4 years. Then the amount of remaining radioactive material is
$0.5 \mathrm{~g}$
$0.125 \mathrm{~g}$
$0.25 \mathrm{~g}$
$0.0625 \mathrm{~g}$
Solution
Half life, $\mathrm{T}_{1 / 2}=2$ year
Quantity of substance, $\mathrm{N}_0=1 \mathrm{~g}$
Using law of radio activity, $\mathrm{N}=\mathrm{N}_0 \mathrm{e}^{-\lambda \mathrm{t}}$
Decay constant, $\lambda=\frac{0.693}{\mathrm{~T}_{1 / 2}}$
$\begin{aligned}
& =\frac{0.693}{2}=0.346 \\
& =0.35 \text { per year } \\
& \text { Thus, } \mathrm{N}=1 \times \mathrm{e}^{-0.35 \times 4}=0.25 \mathrm{~g}
\end{aligned}$