The number of half lives elapsed before $93.75 \%$ of a radioactive sample has decayed is
The number of half lives elapsed before $93.75 \%$ of a radioactive sample has decayed is
6
4
2
8
Solution
Number of half lives be obtained by using
$\begin{array}{llll}
N =N_0\left(\frac{1}{2}\right)^n \\
\text {Here, } N =(100-93.75) \times \frac{N_0}{100}=\frac{6.25}{100} \times N_0 \\
\therefore \left(\frac{1}{2}\right)^n =\frac{625}{10000}=\left(\frac{5}{10}\right)^4=\left(\frac{1}{2}\right)^4 \\
\text {or } n =4
\end{array}$