Question

A certain sample of a radioactive material decays at the rate of 500 per second at a certain time. The count rate falls to 200 per second after 50 minutes. (a) What is the decay constant of the sample ? (b) What is its half-life ?

Answer 1

Given A = 200,

$A_0=500,t=50\text{min}$

$A=A_0{e}^{-\lambda \tau }$

$\text{or}200=500\times e^{-50\times 60\times \lambda }$

$\Rightarrow \frac{2}{5}=e^{-3000\lambda }$

$\Rightarrow ln\frac{2}{5}=-3000\lambda$

$\Rightarrow \lambda =3.05\times {10}^{-94}S$

(b) $t_{\frac{1}{2}}=\frac{0.693}{\lambda }=2272.13\text{sec}$

= $38\text{min}$