Nuclei - Result Question 67
68. The half life of a radioactive isotope ’ $X$ ’ is 50 years. It decays to another element ’ $Y$ ’ which is stable. The two elements ’ $X$ ’ and ’ $Y$ ’ were found to be in the ratio of $1: 15$ in a sample of a given rock. The age of the rock was estimated to be
[2011]
(a) 150 years
(b) 200 years
(c) 250 years
(d) 100 years
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Answer:
Correct Answer: 68. (b)
Solution:
- (b) Let number of atoms in $X=N_x$
Number of atoms in $Y=N_y$
By question
$\frac{N_x}{N_y}=\frac{1}{15}$
$\therefore$ Part of $N_x=\frac{1}{16}(N_x+N_y)$
$=\frac{1}{2^{4}}(N_x+N_y)$
So, total 4 half lives are passed, so, age of rock is $4 \times 50=200$ years
