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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 1 : 7 in a sample of a given rock. The age of the rock is estimated to be:
A
100 years
B
40 years
C
60 years
D
80 years
Detailed Solution
$\frac{N_x}{N_y} = \frac{1}{7} \Rightarrow \frac{N_x}{N_x + N_y} = \frac{N}{N_0} = \frac{1}{8}$
Using $N = N_0e^{-\lambda t}$: $\frac{N_0}{8} = N_0e^{-\lambda t}$, i.e. three half-lives have passed.
$t = 3\times20$ years = 60 years
Using $N = N_0e^{-\lambda t}$: $\frac{N_0}{8} = N_0e^{-\lambda t}$, i.e. three half-lives have passed.
$t = 3\times20$ years = 60 years