The isotope of `U^(238) and U^(235)` occur in nature in the ratio `140:1`. Assuming that at the time of earth's formation, they were present in equal ratio, make an estimate of the age of earth. The half lives of `U^(238)` and `U^(235)` are `4.5xx10^9` years and `7.13xx10^8` years respectively. Given `log_(10)140=2.1461 and log_(10)2=0.3010.`

Answer

`6.04 xx 10^(9) yrs`

Explanation

Let the age of Earth be `t_("year")` and initially both were present as `N_(0)`,
`Nu_(238)=N_(0)/2^(1//t_(1//2))=N_(0)/(2^(t//4.5xx10^(3)))`
`Nu_(235)=N_(0)/(2^(t//4.3xx10^(8)))`
`(Nu_(238))/(Nu_(235))=140/1=2^(t[1.18xx10^(-9)])`
`t=6.0418xx10^(9)` years