`._(92)^(238)U` by successive radioactive decay changes to `._(82)^(206)Pb`. A sample of uranium ore was analysed and found to contain 1.0g of `.^(238)U` and 0.1g of `.^(206)Pb`. Assuming that all `.^(206)Pb` hasaccumulated due to decay of `.^(238)U`, find the age of the ore (half life of `.^(238)U=4.5xx10^(9)` yrs).

Explanation

Number of moles of `.^(238)U = (1)/(238)`
Number of moles of `.^(206)Pb = (0.1)/(206)`
Applying the relationship,
`t = (2.303/(lambda) log [1 + (.^(206)Pb)/(.^(238)U)]`
`= (2.303)/(0.693) xx 4.5 xx 10^(9) log [1 + ((0.1)/(206))/((1)/(238))] = 7.098 xx 10^(8)` years