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=0.231s^(-1)`
b) `N=N_(0)^(-lamdat_(1))` (or)
`t_(1)=1/lamdalog_(e)""N_(0)/N`
`=1/(0.231)log_(e)""(8000)/1000`
= 9 sec
`|(dN)/(dt)|_(t=t_(1))=lamdaN=0.231xx1000=231 s^(-1)`