Q 12-13-115JEE MainJEE Main 2020 (7 Jan, Shift 2)Medium
The activity of a radioactive sample falls from $700\ \text{s}^{-1}$ to $500\ \text{s}^{-1}$ in $30$ minutes. Its half life is close to:
Answer: (B) $62$ min
$A = A_0e^{-\lambda t}$:
$$\lambda = \frac{1}{30}\ln\frac{700}{500} = \frac{\ln1.4}{30} \approx \frac{0.336}{30}\ \text{min}^{-1}$$
$$T_{1/2} = \frac{0.693}{\lambda} = \frac{0.693\times30}{0.336} \approx 62\ \text{min}$$
Solution by Sreeraj P, M.Sc Physics