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)=4.5xx10^(9)y`
`=4.5xx10^(9)y xx 3.16xx10^(7)s//y`
`= 1.42xx10^(17)s`
One k mol of any isotope contains Avogadro's number of atoms, and so 1 g of `._(92)^(238)U` contains
`(1)/(238xx10^(-3))kmol xx 6.025xx10^(26)` atoms/kmol
`= 25.3xx10^(20)` atoms.
The decay rate R is
`R = lambda N`
`= (0.693)/(T_(1//2))N=(0.693xx25.3xx10^(20))/(1.42xx10^(17))S^(-1)`
`= 1.23xx10^(4)S^(-1)`
`= 1.23xx10^(4)Bq`