Q 12-13-109JEE MainJEE Main 2021 (25 Jul, Shift 2)Easy
The nuclear activity of a radioactive element becomes $\left(\frac{1}{8}\right)^{\text{th}}$ of its initial value in $30$ years. The half-life of radioactive element is ______ years.
Numerical value type. Enter your answer.
Answer: 10
$\dfrac{1}{8} = \left(\dfrac{1}{2}\right)^3$, so $30$ years is three half-lives: $T_{1/2} = 10$ years.
Solution by Sreeraj P, M.Sc Physics