Q: The radioactive isotope X with a half life of 109 years decays to Y which is stable. A sample of rocks was found to contain both the elements X and Y in the radio 1∶ 7. What is the age of the rocks ?
(a) 2 × 109 Y
(b) 3 × 109 Y
(c) 6 × 109 Y
(d) 7 × 109 Y
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Ans: (b)
Sol: $ \displaystyle \frac{N}{N_0} = \frac{1}{1+7} $
$ \displaystyle \frac{N}{N_0} = \frac{1}{8} = (\frac{1}{2})^3$
As we know , $ \displaystyle \frac{N}{N_0} = (\frac{1}{2})^n $
On comparing we get,
n= 3
t = n T
= 3 × 109 Y