JEE PYQ: Nuclear Physics Question 18
Question 18 - 2020 (07 Jan Shift 2)
The activity of a radioactive sample falls from 700 s$^{-1}$ to 500 s$^{-1}$ in 30 minutes. Its half life is close to:
(1) 72 min
(2) 62 min
(3) 66 min
(4) 52 min
Show Answer
Answer: (2)
Solution
We know that Activity, $A = A_0 e^{-\lambda t}$ $\left(\because \lambda = \frac{\ln 2}{t_{1/2}}\right)$ $A = A_0 e^{-t(\ln 2)/t_{1/2}}$ $\Rightarrow 500 = 700 \cdot e^{-t(\ln 2)/T_{1/2}}$ $\Rightarrow \ln\frac{7}{5} = \frac{30 \ln 2}{T_{1/2}}$ ($\because t = 30$ minute) $\Rightarrow T_{1/2} = 30 \cdot \frac{\ln 2}{\ln 1.4} = 61.8$ minute ($\because \ln 2 = 0.693$ and $\ln 1.4 = 0.336$) $\Rightarrow T_{1/2} \approx 62$ minute
BETA
