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On analysis a sample of Uranium was fou...

On analysis a sample of Uranium was found to contain 0.2777 g of `""_(82)Pb^(206)` and 1.667 g of `""(92)U^(238)`. The half-life periodof `""_(92)^(238)` is `4.51 xx 10^(9)` years. If all the lead were assumed to have come from decay of `""_(92)^(238)`, What is the age of the earth ?

A

`1.143 xx 10^(7)` yrs

B

`1.43 xx 10^(9)` yrs

C

`1.14 xx 10^(5)` yrs

D

`1.143 xx 10^(9)` yrs

Text Solution

Verified by Experts

The correct Answer is:
D
`""_(92)U^(238) = 1.667 g = (1.667)/(238) "mole "_(82)Pb^(206) = 0.227 g = (0.227)/(206)"mole"`
`because` All the lead have come from decay of U.
`therefore` Moles of Pb formed ` = (0.227)/(206) " "therefore` Moles of U decayed ` = (0.227)/(206)`
`therefore` Total moles of Uranium present initially ` = (1.667)/(238) + (0.277)/(206)`, ie, `N_(0)`
Also N for `U^(238) = (1.667)/(238) because` For `U^(238), t = (2.303)/(K) log "" (N_(0))/(N) = (2.303 xx 4.51 xx 10^(9))/(0.693) log "" ((1.667)/(238) + (0.277)/(206))/((1.667)/(138))`
`t = 1.143 xx 10^(9)` yrs
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