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A radioactive nucleus is being prodouced...

A radioactive nucleus is being prodouced at a constant rate `alpha` per second. Its decay constant is `lamda`. If `N_(0)` are the number of nuclei at time t =0 then maximum number of nuclei possible are

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Factory `underset(const.rate)overset(R) rarr A underset(decay)overset(lambda) rarrB`
Let `N` be the number of nuclei of A any time t.
`because (dN)/(dt)=R-lambdaN" "underset(0)overset(N)(int)(dN)/(R-lambdaN)=underset(0)overset(t)(int)dt`
On solving, we will get
`N = R//lambda (1-e^(-lambda t))`
(b) Number of nuclei of B at any tiem t,
`N_(B) =Rt -N_(A)`
`=R t-R//lambda(1-e^(-lambda t) )=R//lambda(lambda t -1 +e^(- lambda t))`
Maximum number of nuclei of ''A'' present at any time during its formation ` =R//lambda` .
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