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
  1. 6
  2. 4
  3. 2
  4. 8

Solution

Number of half lives be obtained by using $\begin{array}{llll} N =N_0\left(\frac{1}{2}\right)^n \\ \text {Here, } N =(100-93.75) \times \frac{N_0}{100}=\frac{6.25}{100} \times N_0 \\ \therefore \left(\frac{1}{2}\right)^n =\frac{625}{10000}=\left(\frac{5}{10}\right)^4=\left(\frac{1}{2}\right)^4 \\ \text {or } n =4 \end{array}$

Asked in: AP EAMCET 2018 (23 Apr Shift 2)

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