Question

One gram of a radioactive substance takes 50 s to lose 1 centigram. Find its half-life period

Answer 1

Using law of radio activity , $N=N_0{e}^{-\lambda t}$

Here, $N_0=1$ gram and rest substance after decay $N=(1-1/100)=0.99$ gram ; $t=50s$

Now, $0.99=e^{-50\lambda }$ or $e^{50\lambda }=1/0.99$

Taking ln, $50\lambda =ln1-ln0.99=0-(-0.01)=0.01$

$\lambda =0.0002s^{-1}$

Half life $t_{1/2}=0.693/\lambda =0.693/0.0002=3465s$