On analysis a sample of uranium are was found to contain 227g of `._(82)Pb^(208)` and 1.667 g of `._(92)U^(238)`. The half life peiod of `U^(238)` is `4.51 xx 10^(9)` yrs. If all the lead was assumed to have come from decay of `._(92)U^(238)`, what is the age of the earth?

Explanation

Mole of `U^(238) = (1.667)/(238)`
Moles of `Pb^(206) = (0.277)/(206)`
`N_(0) = (1.667)/(238) + (0.277)/(206)`
`N = (1.667)/(238)`
`t = (2.303)/(lambda) log (N_(0))/(N)`
`= (2.303 xx 4.51 xx 10^(9))/(0.693) log_(10) ((1.667)/(238) + (0.277)/(206))/((1.667)/(238))`
`= 1.143 xx 10^(9)` years