Question

After an interval of one day, $\frac{1}{16}th$ initial amount of a radioactive material remains in a sample. Then, its half-life is

• A. $6h$
• B. $12h$
• C. $1.5h$
• D. $3h$

Answer 1

The correct option is A $6h$

First order decay:
$N=N_o{e}^{-\lambda t}$
Given at $t=1day$, $N\left(t\right)=\frac{N_o}{16}$
$\frac{N_o}{16}=N_o{e}^{-\lambda }$
$\lambda =ln16da{y}^{-1}$

Half life, $t_{1/2}=\frac{ln2}{\lambda }=\frac{ln2}{ln16}=24/4=6hours$