Question

A radioactive substance decays to ${\left(\frac{1}{16}\right)}^{th}$ of its initial activity in $80$ days. The half life of the radioactive substance expressed in days is ______.

Answer 1

$N_0\stackrel{t_{1/2}}{\to }\frac{N_0}{2}\stackrel{t_{1/2}}{\to }\frac{N_0}{4}\stackrel{t_{1/2}}{\to }\frac{N_0}{8}\stackrel{t_{1/2}}{\to }\frac{N_0}{16}$

$\therefore 4\times t_{1/2}=80$

$\Rightarrow t_{1/2}=20$ days