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

Explanation

`T_(1//2) = 4.5 xx 10^9 y = 4.5 xx 3.16 xx 10^7 s//y`
`= 1.42 xx 10^(17) s`
One k mol of any isotope contains Avogadro.s number of atoms, and so 1g of `""_(92)^(238)U` contains `1/(238 xx 10^(-3)) kmol xx 6.025 xx 10^(26) "atom"//kmol = 25.3 xx 10^(20) "atoms"`
The decay rate R is `R = lambda N = (0.693)/(T_(1//2)) N`
`= (0.693 xx 25.3 xx 10^(20))/(1.42 xx 10^(17)) s^(-1) = 1.23 xx 10^4 s^(-1) = 1.23 xx 10^4 Bq`.