A radioactive isotope X has a half-life of 3s. At t = 0 s, a given sample of this isotope X contains 8000 atoms. Find the time `t_(1)`, when 1000 atoms of isotope X remains in the sample.

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)`