Question

A radioactive isotope has a half-life of $2$ years. How long will it approximately take the activity to reduce to $3\%$ of its initial value?

• A. $4.8Years$
• B. $7Years$
• C. $10Years$
• D. $9.6Years$

Answer 1

The correct option is C $10Years$

$\begin{array}{c}=N_0{\left(\frac{1}{2}\right)}^n\\ \text{Here,}\text{N is final activity.}\\ \text{No is initial activity.}\\ \text{Given:}\frac{N}{N_0}=\frac{3}{100}\\ \therefore \frac{3}{100}={\left(\frac{1}{2}\right)}^n\\ 2^n=33.33\\ n\simeq 5\end{array}$

$\begin{array}{c}\therefore \text{Activity reduces to}3\%\text{of initial}\\ \text{value of}5\text{half lives that is}10\text{years.}\end{array}$