Nuclear Physics And Radioactivity Question 60
Question: A radioactive isotope X with a half-life of $ 1.37\times 10^{9} $ years decays to Y which is stable. A sample of rock from the moon was found to contain both the elements X and Y which were in the ratio of 1 : 7. The age of the rock is
Options:
A) $ 1.96\times 10^{8} $ years
B) $ 3.85\times 10^{9} $ years
C) $ 4.11\times 10^{9} $ years
D) $ 9.59\times 10^{9} $ years
Show Answer
Answer:
Correct Answer: C
Solution:
If in the rock there is no Y element, then the time taken by element X to reduce to $ \frac{1}{8}th $ the initial value will be equal to $ \frac{1}{8}={{( \frac{1}{2} )}^{n}} $ or n =3 Therefore, from the beginning three half life time is spent. Hence the age of the rock is $ =\lambda N=\lambda N_{0}{{( \frac{1}{2} )}^{\frac{9}{3}}}=\frac{\lambda N_{0}}{8} $ .
BETA
