Question

The activity of a radioactive sample decreases by $87.5$% of the initial value after $60$ days.The half life of the sample will be:

• A. $100$days
• B. $60$days
• C. $30$days
• D. $20$days

Answer 1

The correct option is D $20$days

Decreases by $87.5\%$

$\Rightarrow$ Remainder $=100-87.5$

$=12.5\%$

If initiate activity$=A_o$ then remainder $A=A_o\times \frac{2.5}{100}=\frac{A_o}{8}$

Using relation $A=A_o{\left(\frac{1}{2}\right)}^n$

We get $\frac{A_o}{2}=A_o{\left(\frac{1}{2}\right)}^n$

$\Rightarrow n=3$

Time $=60$ days

$\Rightarrow$ Half life $=\frac{60}{n}=\frac{60}{3}=20$ days.