The half of `.^(238)U` decomposed to `.^(206)Pb` in `4.5xx10^(8)` year. What will be the age of rock that contains equal weight of both?

Explanation

`{:(,U^(238),rarr,Pb^(208)),("No of atom at t"=0,N_(0),,0),("No of atom at t"=t,N_(0)-N,,N),("Wt of metal at t"=t,w,,w):}`
`:' N_(U)` left `= (w)/(238)`
`N_(Pb)` formed `= (w)/(206)`
`N_(OU) = (w)/(238) + (w)/(206)`
Now, `t = (2.303)/(lambda) log (N_(OU))/(N_(U))`
`= (2.303xx4.5xx10^(8))/(0.693)` log `((w)/(238) + (w)/(206))/((w)/(238))`
`=n 4.99xx10^(8) yr`.