JEE PYQ: Nuclear Physics Question 21
Question 21 - 2019 (10 Apr Shift 1)
Two radioactive materials A and B have decay constants $10\lambda$ and $\lambda$, respectively. If initially they have the same number of nuclei, then the ratio of the number of nuclei of A to that of B will be $1/e$ after a time:
(1) $\frac{1}{9\lambda}$
(2) $\frac{1}{11\lambda}$
(3) $\frac{11}{10\lambda}$
(4) $\frac{1}{10\lambda}$
Show Answer
Answer: (1)
Solution
As $N = N_0 e^{-\lambda t}$ So, $\frac{N_A}{N_B} = e^{(\lambda_B - \lambda_A)t} = \frac{1}{e} \Rightarrow (\lambda_B - \lambda_A)t = -1$ $\Rightarrow (\lambda_A - \lambda_B) \cdot t = 1$ $\Rightarrow t = \frac{1}{(\lambda_B - \lambda_A)} = \frac{1}{10\lambda - \lambda} = \frac{1}{9\lambda}$
BETA
