Question

The half-life of a certain radioactive isotopes is $32h$. What fraction of a sample would remain after $16h$?

• A. $0.25$
• B. $0.71$
• C. $0.29$
• D. $0.75$

Answer 1

The correct option is B $0.71$

$t_{1/2}=32hrs$

Decay constant $=\lambda =\frac{ln2}{32}$
Also, $N\left(t\right)=N_o{e}^{-\lambda t}$
At $t=16hours$
$N=N_o{e}^{-16\frac{ln2}{32}}$
$N=\frac{1}{\sqrt{2}}{N}_o=0.707N_o$