JEE PYQ: Nuclear Physics Question 22
Question 22 - 2019 (10 Apr Shift 2)
Two radioactive substances A and B have decay constants $5\lambda$ and $\lambda$ respectively. At $t = 0$, a sample has the same number of the two nuclei. The time taken for the ratio of the number of nuclei to become $\left(\frac{1}{e}\right)^2$ will be:
(1) $1/2\lambda$
(2) $1/4\lambda$
(3) $1/\lambda$
(4) $2/\lambda$
Show Answer
Answer: (1)
Solution
Let $N_1$ and $N_2$ be the number of radioactive nuclei of substance at anytime $t$. $N_1(\text{at } t) = N_0 e^{-5\lambda t}$ …(i) $N_2(\text{at } t) = N_0 e^{-\lambda t}$ …(ii) Dividing equation (i) by (ii), we get $\frac{N_1}{N_2} = \frac{1}{e^2} = e^{-4\lambda t}$ $\Rightarrow 4\lambda t = 2$ $\Rightarrow t = \frac{2}{4\lambda} = \frac{1}{2\lambda}$
BETA
