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Uranium ._(92)U^(238) decayed to ._(82)Pb^(206). They decay process is ._(92)U^(238) underset((x alpha, y beta))(rarr ._(82)Pb^(206)) t_(1//2) of U^(238)= 4.5 xx 10^(9) years A sample of rock south America contains equal number of atoms of U^(238) and Pb^(206). The age of rock will be

Answer»

`4.5 xx 10^(9)` years
`9 xx 10^(9)` years
`13.5 xx 10^(9)` years
`2.25 xx 10^(9)` years

Solution :`K = (2.303)/(t) "log" ((N_(0))/(N))`
`(0.693)/(t_(1//2)) = (2.303)/(t) "log" ((N_(0))/(N))``[{:(N_(0) = 1 + 1 = 2),(N = 1):}]`
`(0.693)/(4.5 xx 10^(9)) = (2.303)/(t) "log" ((2)/(1))`
`:.t = 4.5 xx 10^(9)` years


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