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)`lambda=0.693/T_(1//2) = 0.693/3=0.231 s^(-1)`
(b)`N=N_0e^(-lambdat)`
`t_1=1/lambda log_e N_0/N = 1/0.231 log_e 8000/1000`=9 sec
(c)`|(dN)/(dt)|_(t=t_1)=lambdaN=0.231xx1000=231 s^(-1)`