The half life of `._92U^(238)` against `alpha` -decay is `4.5xx10^9` years. What is the activity of 1g sample of `._92U^(238)`?

Explanation

`T_(1//2)=4.5xx10^(9)y`
`=4.5xx10^(9)yxx3.16xx10^(7)s//y`
`=1.42xx10^(17)s`One k mol of any isotope contains Avogadro’s number of atoms, and so 1g of `._(92)238)U` contains
`(1)/(238xx10^(-3)kmolxx6.025xx10^(26)` atoms /Kmol
`=25.3xx10^(20)` atoms.
The decay rate R is
R = λN
`=(0.693)/(T_(1//2)N=(0.693xx25.3xx10^(20))/(1.42xx10^(17))s^(-1)`
`=1.23xx10^(4)s^(-1)`
`=1.23xx10^(4)Bq`