A radicactive sample consider of two distinct species having equial number initially . The mean life time of one species is `tau` and that of the other is `5 tau` . The decay prodects in both cases are stable . A plot is made of the total number of radioactive nuclei as a function of time , which of the following figure best represent the from of this plot?
A
B
C
D
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The correct Answer is:
D
`N_(1) = N_(oe)^(-lambda _(1) t = N_(0e) ^(t/tau)` ….(i) `as tau = (1)/(lambda_(1))` `N_(2) = N_(0e) ^(-lambda_(2)t) = N_(0e) ^(t/5tau) ` ….(i) as `5 tau = (1)/(lambda_(2))` Adding (i) and (ii) we get `N = N_(1)+ N_(2) = N_(0)(e^(-t//tau) + e^(-t//5 tau) ) (a) in NOT the carrect option as there is a time `tau` for which `N` is constant which means for time `tau` there is no process of radioactivity which does not make same . (b) and (c ) shown intermediate increase in the numberof radicacitive atom which is IMMPOSSIBLE as `N` willl only decrease exponentially.
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