Question

The initial activity of a certain radioactive isotopes was measured as $16000$ counts $mi{n}^{-1}$. Given that the only activity measured was due to this isotopes and that its activity after $12h$ was $2100$ counts $mi{n}^{-1}$, its half-life, in hours, is nearest to [Given $lo{g}_e\left(7.2\right)=2]$

• A. $9.0$
• B. $6.0$
• C. $4.0$
• D. $3.0$

Answer 1

The correct option is C $4.0$

Activity $=\frac{dN}{dt}=N_o\lambda e^{-\lambda t}$
Let initial activity be, $A_o=16000mi{n}^{-1}$
$A\left(t\right)=$ $A_0{e}^{-\lambda t}$
At $t=12hr$
$2100=16000e^{-12\lambda }$
$\lambda =0.169h{r}^{-1}$

Half life: $t_{1/2}=\frac{ln2}{\lambda }=4hrs$