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  • 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

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

Option: 1

150 years


Option: 2

200 years


Option: 3

250 years


Option: 4

100 years


Answers (1)

best_answer

Let number of atoms in \mathrm{X}=\mathrm{N}_{\mathrm{X}}

Number of atoms in \mathrm{Y}=\mathrm{N}_{\mathrm{y}}

By questions  \frac{\mathrm{N}_{\mathrm{x}}}{\mathrm{N}_{\mathrm{y}}}=\frac{1}{15}

\therefore \quad \text { Part of } \mathrm{N}_{\mathrm{x}}=\frac{1}{16}\left(\mathrm{~N}_{\mathrm{x}}+\mathrm{N}_{\mathrm{y}}\right)=\frac{1}{2^4}\left(\mathrm{~N}_{\mathrm{x}}+\mathrm{N}_{\mathrm{y}}\right)

So, total 4 half lives are passed, so, age of rock is  4 \times 50=200 years. 

Posted by

Ritika Harsh

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