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State the law of radioactivity and hence...

State the law of radioactivity and hence, show that `N=N_(0)e^(-lambda t)`.

Text Solution

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(a) `(dN)/( dt) = - lambda N`
`int_(N_0)^(N) (dN)/( N) = int_(0)^(t) -lambda dt`
`[log_(e)^(N) ]_(N_0)^(N) = - lambda [t]_(0)^(t)`
`log_(e) (N)/(N_0)=- lambda t`
`N=N_(0) e^(- lambda t)`
(b) (i) `""{:(22),(11):} Na to {:(22),(11):} Ne + e^(+) +v`
or, `{:(22),(11):} Na to {:(22),(11):} Xe + e^(+) + v`
Basic process
`p to n + e^(+) + v`
(ii) Isobar.
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