The half life of a radioactive substance is 30 days. The time taken for ${\left(\frac{3}{4}\right)}^{\mathrm{th}}$ of its original mass to disintegrate, is:

The number of substance that will be left after ${\left(\frac{3}{4}\right)}^{\mathrm{th}}$ of its original substance disintegrated will be:

$\mathrm{N}={\mathrm{N}}_0-\frac{3{\mathrm{N}}_0}{4}=\frac{{\mathrm{N}}_0}{4}$

$\frac{\mathrm{N}}{{\mathrm{N}}_0}={\left(\frac{1}{2}\right)}^{\mathrm{n}}\text{ gives }\frac{1}{4}={\left(\frac{1}{2}\right)}^{\mathrm{n}}\text{ or }\mathrm{n}=2$

  $\therefore \text{ Time taken }=n\times T_{1/2}=2\times 30\text{ days }=60\text{ days. }$