The half-life of `._(92)^(238)U` undergoing `alpha` - decay is `4.5xx10^(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 10^9 y xx 3.16 xx 10^(7) s//y`
`= 1.42 xx 10^(17) s`
One kmol of any isotope contains Avogadro.s of atoms, and so 1g of `""_(92)^(238)U` contains
`(10^(-3))/(238) "kmol" xx 6.025 xx 10^(26) "atoms/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`.