Question

The half life of a radioactive element is $10$ hrs. How much be left after $4$ hrs in $1$ gm atom sample?

Answer 1

$\frac{4}{10}\Rightarrow 0.4$ left lives
after $0.4$ half lives
The amount would be left

$={\left(\frac{1}{2}\right)}^{0.4}$
$={\left(\frac{1}{2}\right)}^{0.4}\times 1gm$
$=\frac{1}{2}$