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



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