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The age of a rock containing lead and ur...

The age of a rock containing lead and uranium is equal to `1.5xx10^(9)` years. The uranium is decaying into lead with half-life equal to `4.5xx10^(9)` years. Find the ratio of lead to uranium present in the rock, assuming initially no lead was present in the rock.
(Given : `2^(1//3)=1.259`)

Text Solution

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Let `N_(0)`, be the number of uranium nuclides present at the initial moment of time and `N_(u)andN_(Pb)` be the number of uranium and lead nuclides present.
Now `N_(u)/N_(0)=(1/2)^(t//T_(1//2))=(1/2)^(1//3)=1/1.259`
`(Nu)/(N_(u)+N_(Pb))=1/(1.259)`
or `(Nu)/(N_(u)+N_(Pb))=1.259`
or `(Nu)/(N_(u)+N_(Pb))-1=1.259-1`
or `N_(Pb)/N_(u)=0.259`.
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