The half life of a radioactive substance is 20 s. The time taken for its sample to decay 7/8th of the initial value

60 s

The correct answer is Option (3) → 60 s

Given half-life,

$T_{1/2} = 20\text{ s}$

Fraction of undecayed nuclei =

$1 - \frac{7}{8} = \frac{1}{8}$

Using relation,

$\frac{N}{N_0} = \left(\frac{1}{2}\right)^{t/T_{1/2}}$

Substitute

$\frac{N}{N_0} = \frac{1}{8}$

$\frac{1}{8} = \left(\frac{1}{2}\right)^{t/20}$

$\left(\frac{1}{2}\right)^3 = \left(\frac{1}{2}\right)^{t/20}$

$t = 60\text{ s}$

∴ Time taken for the sample to decay 7/8th of its initial value is $60\text{ s}$