1.

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. 40 yearsB. 60 yearsC. 80 yearsD. 100 years

Answer» Correct Answer - B
Half-life of `X rArr T_(X)=20` years
`underset(1)overset("Active")X underset(" ")to underset(7)overset("Stable")Y`
`(N)/(N_(0))=(1)/(1+7)=(1)/(8)=(1)/(2^(n))=(1)/(2^(3))`
`n=3=(t)/(T)=(t)/(20)`
`t=60` years.


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