A sample of `U^(238) ("half life" = 4.5 xx 10^(9)yr)` ore is found to contain `23.8 g" of " U^(238) ` and `20.6g ` of `Pb^(206)`. Calculate the age of the ore

Answer

[`4.5 xx 10^(9)` year]

Explanation

`U^(238) rarr Pb^(206)`
`((20.6)/(206))=0.1 "mol present"`
i.e. 0.1 mol of `U^(238)` decay
`0.1 xx 238=(23.8)` decay
Initial mass of `U^(238)=(23.8 +23.8)=47.6`
23.8 left and 23.8 decay
time `t_(1//2)=4.5 xx 10^(9)` year