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A radioactive isotope X with half-life 1...

A radioactive isotope X with half-life `1.5xx10^9` y decays into a stable nucleus Y. A rock sample contains both elements X and Y in ratio 1:15. Find the age of the rock .

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X `to` Y (stable)
Let the quantity of X and Y in the sample be `N_x` and `N_y` respectively.
`therefore N_x/N_y=1/15` or, `N_x/(N_x+N_y)=1/16`
or ,`N/N_0=1/16` [ `N_0=N_x + N_y` and `N_x=N` ]
We know that, `N=N_0 e^(-lambdat)`
`therefore e^(lambdat)=N_0/N=16`
or, `t="4In2"/lambda=(4In2xxt_(1//2))/"In2" [ because lambda="In2"/t_(1//2)]`
or, `t=4xx1.5xx10^9 y = 6xx10^9` y
`therefore` Age of the rock =`6xx10^9` y.
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