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?

Answer: DSolution: `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.