Half life of `""^(226)Ra` is `1600` years. How many distintegrations per second occur in 1 gram of `""^(226)Ra` ?

Explanation

Data supplied,
`T_(1//2) = 1600 yrs, lambda = 0.6931//T_(1//2)`
No. of atoms in one gram of `Ra^(226), N = (1 xx 10^(-3))/(226) xx 6.023 xx 10^(23)`
`(dN)/(dt) = lambda N = (0.6931)/(1600) xx (6.023 xx 10^(20))/(226) = 1.1545 xx 10^(15)` per year
`i.e, (dN)/(dt) = 3.661 xx 10^7 "per sec" = (3.661 xx 10^7)/(3.7 xx 10^(10)) = 0.99 xx 10^(-3) Ci`