Atoms And Nuclei Question 375
Question: 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
Options:
A) 150 years
B) 200 years
C) 250 years
D) 100 years
Show Answer
Answer:
Correct Answer: B
Solution:
-
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
