JEE PYQ: Nuclear Physics Question 2
Question 2 - 2021 (16 Mar Shift 2)
Calculate the time interval between 33% decay and 67% decay if half-life of a substance is 20 minutes.
(1) 60 minutes
(2) 20 minutes
(3) 40 minutes
(4) 13 minutes
Show Answer
Answer: (2)
Solution
$N_1 = N_0 e^{-\lambda t_1}$, $\frac{N_1}{N_0} = e^{-\lambda t_1}$ $0.67 = e^{-\lambda t_1}$, $\ln(0.67) = -\lambda t_1$ $N_2 = N_0 e^{-\lambda t_2}$, $0.33 = e^{-\lambda t_2}$, $\ln(0.33) = -\lambda t_2$ $\ln(0.67) - \ln(0.33) = \lambda t_1 - \lambda t_2$ $\lambda(t_1 - t_2) = \ln\left(\frac{0.67}{0.33}\right)$ $\lambda(t_1 - t_2) \cong \ln 2$ $t_1 - t_2 \simeq \frac{\ln 2}{\lambda} = t_{1/2} = 20$ minutes.
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