Nuclei - Result Question 63
64. The half life of a radioactive isotope ’ $X$ ’ is 20 years. It decays to another element ’ $Y$ ’ which is stable. The two elements ’ $X$ ’ and ’ $Y$ ’ were found to be in the ratio of $1: 7$ in a sample of a the given rock. The age of the rock is estimated to be
[2013]
(a) 60 years
(b) 80 years
(c) 100 years
(d) 40 years
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Answer:
Correct Answer: 64. (a)
Solution:
- (a) The value of $x$ is $\frac{1}{8}$ $=\frac{x_0}{8}=\frac{x_0}{2^{3}} \Rightarrow t=3 T=3 \times 20=60$ years Hence the estimated age of the rock is 60 years
$ \begin{aligned} & X \to Y_0 \\ & \text{ at } t=0 \quad N_0 \quad 0 \\ & \text{ at } t=t \quad N \quad N_0-N \end{aligned} $
$ \begin{aligned} & \frac{N}{N_0-N}=\frac{1}{7}=\frac{N}{N_0}=\frac{1}{8} \\ & t=3 T \\ & =3 \times 20=60 \text{ years } \end{aligned} $
