`U^(238)` is found to be in secular equilibrium with `Ra^(226)` in its ore. If chemical analysis shown `1` atoms of `Ra^(226)` per `2.8xx10^(6)` atoms of `U^(238)`, find the half-like of `U^(228)`. Given the half life `Ra^(226)` is `1620` years.

Explanation

For secular equilibrium
`lambda_(U)N_(U) = lambda_(Ra)N_(Ra)`
`(ln2)/((T_(1//2))_(U))N_(U) = (ln2)/((T_(1//2))_(Ra))N_(Ra)`
`(2.8xx10^(6))/((T_(1//2))_(U)) = (1)/(1620)`
`(T_(1//2))_(U) = 4.5 xx 10^(9)` year