A radioactive isotope X has a half life of 3 seconds. At t=0, a given sample of this isotope contains 8000atom. Calculate (i) its decay constant (ii) average time (iii) the time `t_1`, when 1000 atoms of the isotope X remain in the sample (iv) number of decay/sec in the sample at `t=t_1sec.`

Explanation

Here, `T=3s , N_0=8000`
(i) `lambda=0.6931/T=0.6931/3=0.231sec^-1`
(ii) `tau=1/lambda=1/0.231=4.33s` (iii) `N=1000, t_1=?`
As `N/(N_0)=(1/2)^n :. 1000/8000= (1/2)^n :. n=3, t_1=nT=3xx3=9sec.`
(iv) `((dN)/(dt))_(t=t_1)=lambdan=0.231xx1000=231s^-1`