Counting rate from a radioactive source is 8000 cts per sec. at time t = 0 and after 10 minutes decay is 1000 cts/sce. Calculate (i) half life period, (ii) decay constant and (iii) counting rate after 20 minutes.

Explanation

Data supplied,
i `N_0 = 8000 cts//"sec", " " t_1 = 10 "minutes", " " N = 1000 cts//"sec"`
`N/(N_0) = 1/(2^n)`
`:. 1/(2^n) = 1000/8000 = 1/8 = 1/(2^3)`
`:. 2^n = 2^3 , " " n = 3`
`t_1 = nT_(1//2) " " :. " " T_(1//2) = (t_1)/n= 10/3 "minutes" = 200 "sec"`
i.e. Half life period = `10/3` minutes = 200 sec
ii. Decay constant `lambda = (0.6931)/((10//3)) = 0.2079` per minute
iii. `t_2 = 20 "min" :. t_2 = nT, " " n = (t_2)/(T_(1//2)) = 20/((10//3)) = 6`
`:. N/(N_0) = 1/(2^n) = 1/(2^6) = 1/64`
`N = (N_0)/64 = 8000/64 = 125 cts//"sec"` .