Question

The radioactivity of an old sample of a liquid due to tritium (half life $12.5$ years) was found to be only about $3$% of that measured in a recently purchased bottle marked $7$ year old. The sample must have been prepared about:

• A. $70$ year
• B. $63.24$ year
• C. $420$ year
• D. $300$ year

Answer 1

The correct option is B $63.24$ year

$\begin{array}{c}Hence,\\ \frac{N}{N_0}=0.03=\left(-\lambda t\right)\\ In\left(0.03\right)=-\lambda t=\frac{-In\left(2\right)\times t}{\frac{T_1}{2}}\\ t=\frac{In\left(0.03\right)\times \frac{T_1}{2}}{-In\left(2\right)}=63.24years\end{array}$

Hence,

option $\left(B\right)$ is correct answer.