The half-life of `" "_(92)^(238)U` undergoing `alpha`-decay is `4.5 xx 10^(9)` years. Find the activity of 1 g sample of `" "_(92)^(238)U`.

Explanation

It is given that `T_(1/2) =4.5xx 10^(9) y =4.5 xx 10^(9) xx 3.154 xx 10^(7)s =1.42xx 10^(17)s`
Number of atoms (or nuclides) of `" "_(92)^(238)U` present in 1 g sample
`N= 1/238xxN_(A) = 1/238xx 6.023 xx 10^(23) = 2.53 xx 10^(20)`
Activity of the sample `R=lambdaN= 0.693/T_(1/2)N = (9.693 xx 2.93 xx10^(20))/(1.42xx10^(7))=1.23 xx 10^(4)s^(-1) = 1.23 xx 10^(4) Bq`