An analysis of the rock shows that the relative number of `Sr^(87)` and `Rb^(87) (t_(1//2)=4.7 xx10^(10)` year) atoms is 0.05 . What is the age of the rock? Assume all the `Sr^(87)` have been formed from `Rb^(87)` only

Explanation

`(.^(87)Rb)/(.^(87)Sr) = (x)/(y) = (1)/(0.052)`
`(x)/(x + y) = (1)/(1.052)`
`(N)/(N_(0)) = (1)/(1.052)`
`lambda = (2.303)/(t) log_(10) (N_(0))/(N)`
`(0.693)/(4.7 xx 10^(10)) = (2.303)/(t) = (2.303)/(t) log_(10) 1.052`
`t = 3.43 xx 10^(9)` years