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Uranium (""(92)U""^(238)) decayed to ""(...

Uranium (`""_(92)U""^(238)`) decayed to `""_(82)Pb""^(206)`. The process is `""_(92)U""^(238)underset(xalpha,ybeta)to.""_(82)Pb""^(206)`
`t""_(1//2)of U""^(238)=4.5xx10""^(9)` years
A sample of rock from South America contains equal number of atoms of `U""^(238)` and `Pb""^(""^(206)`. The age of the rock will be

A

`4.5 xx 10^(9)` years

B

`9 xx 10^(9)` years

C

`13.5 xx 10^(9)` years

D

`2.25 xx 10^(9)` years

Text Solution

Verified by Experts

The correct Answer is:
a
`(0.693)/(t_(1//2)) = (2.303)/(t_("age")) log ((N_(0))/(N))`
`(0.693)/(4.5 xx 10^(9)) = (2.303)/(t_("age")) log ((2)/(1))`
`t_("age") = 4.5 xx 10^(9)` yrs
`N_(0) = 1 + 1 =2, N = 1`
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