### Neet Solved Paper 2013 Question 35

##### Question: The half-life of a radioactive isotope X is 20 yr. It decays to another element Y which is stable. The two elements X and Y were found to be in the ratio 1:7 in a sample of a given rock. The age of the rock is estimated to be

#### Options:

A) 40 yr

B) 60 yr

C) 80 yr

D) 100 yr

## Show Answer

#### Answer:

Correct Answer: B

#### Solution:

- As $ \frac{N}{N _0}={{( \frac{1}{2} )}^{n}} $ $ \frac{N}{N _0}={{( \frac{1}{2} )}^{3}}=\frac{1}{8} $ Number of half lives = 3

$ \Rightarrow $ $ T=20yr $

$ \therefore $ $ T=\frac{t}{n} $ or $ t=T\times n=20\times 3yr=60yr $