Question

A radioactive element has half life period of $30$ days. How much of it will be left after $90$ days?

Answer 1

Total time $=90$ days
Half life $\left(t_{1/2}\right)=30$ days
We know that, total time $=n\times t_{1/2}$
So, $90=n\times 30$
$n=3$
Thus, quantity left after three half life periods $={\left(\frac{1}{2}\right)}^3{N}_0$ [$N_0=$ original amount]
$=\frac{1}{8}\times N_0=\frac{1}{8}{N}_0$