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A sample of uranium mineral was found to...

A sample of uranium mineral was found to contain `Pb^(208)` and `U^(238)` in the ratio of 0.008 : 1. Estimate the age of the mineral (half life of `U^(238)` is `4.51 xx 10^(9)` years).

Text Solution

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`t=(2.303)/(lambda)log[1+(.^(206)Pb)/(.^(238)U)]`
`t=(2.303)/(0.693)xxt_(1//2)xxlog[1+(.^(206)Pb)/(.^(238)U)]`
`implies` Ratio by mass `.^(206)Pb : .^(238)U=0.008 : 1`
Ratio by moles `.^(206)Pb : .^(238)U=(0.008)/(206) : (1)/(238)`
`=0.0092`
`:. t=(2.303xx4.51xx10^(9))/(0.693)log(1+0.0092)` `=(2.303xx4.51xx10^(9))/(0.693)xx0.00397`
`=(0.0412)/(0.693)xx10^(9)=5.945xx10^(7)` years
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