Question

A radioactive material of half-life T was produced in a nuclear reactor at different instants, the quantity produced second time was twice of that produced first time. If now their present activities are $A_{1}and{A}_2$ respectively then their age difference equals

• A. $\frac{T}{In2}|ln\frac{2A_1}{A_2}|$
• B. $T|ln\frac{A_1}{A_2}|$
• C. $\frac{T}{In2}|ln\frac{A_2}{2A_1}|$
• D. $T|ln\frac{A_2}{2A_1}|$

Answer 1

The correct option is C

$\frac{T}{In2}|ln\frac{A_2}{2A_1}|$

$A_1=\lambda N_0{e}^{-\lambda t_1}or{t}_1=\frac{1}{\lambda }ln\left(\frac{\lambda N_0}{A_1}\right)A_2=\left(\lambda \right)\left(2N_0\right)e^{-\lambda t_2}\therefore t_2=\frac{1}{\lambda }ln\left(\frac{2\lambda N_0}{A_2}\right)t_1-t_2=\frac{1}{\lambda }ln\left(\frac{A_2}{2A_1}\right)=\frac{T}{In\left(2\right)}ln\left(\frac{A_2}{2A_1}\right)$