JEE PYQ: Nuclear Physics Question 23
Question 23 - 2019 (12 Apr Shift 2)
Half lives of two radioactive nuclei A and B are 10 minutes and 20 minutes, respectively. If, initially a sample has equal number of nuclei, then after 60 minutes, the ratio of decayed numbers of nuclei A and B will be:
(1) 3 : 8
(2) 1 : 8
(3) 8 : 1
(4) 9 : 8
Show Answer
Answer: (4)
Solution
$\frac{N_1}{N_2} = \frac{N_0(1 - e^{-2\lambda t})}{N_0(1 - e^{-\lambda t})}$ or $\frac{N_1}{N_2} = \frac{1 - e^{\frac{-0.693}{10} \times 60}}{1 - e^{\frac{-0.693}{20} \times 60}} = \frac{1 - e^{-4.2}}{1 - e^{-2.1}} = \frac{9}{8}$
BETA
