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The half-life of a radioactive isotope X...

The half-life of a radioactive isotope `X` is `20` 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 : 7` in a sample of a given rock. The age of the rock was estimated to be.

A

`100yr`

B

`40yr`

C

`60yr`

D

`80yr`

Text Solution

Verified by Experts

The correct Answer is:
C
Here, T=20 yrs, `(N_(x))/(N_(y))=1/7, t=?`
Now, `(N_(x))/(N_(x)+N_(y))+1/(1+7)=1/8 =N/(N_(0))`
form `N/(N_(0)) =1/8= (1/2)^(n), n=3`
`:. t=nT=3xx20yrs =60yrs`
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