A radioactive isotope X has a half life of 3 second Initially a given sample of this isotope contains 8000 atoms. Calculate (a) its decay constant , (b) the time `t_1` when 1000 atoms of the isotope X remain in the sample , and (c) the number of decay per second in the sample at `t =t_1`.

Explanation

(a) `lamda=(0.693)/(T_(1//2))=(0.693)/3=0.231 s^(-1)`
(b) `N= N_(0)e^(-lamdat_(1))` (or)
`t_(1) = 1/lamdalog_(e) ""N_(0)/N = 1/(0.231) log_(e)""(8000)/1000=9 sec`
(c) `|(dN)/(dt)|_(t=t_(1))= lamdaN=0.231 xx 1000 = 231 s^(-1)`