Radium being a member of the uranium series occurs in uranium ores. If the half lives of uranium and radium are respectively `4.5 xx 10^(9)` and `1620` years calculate the `(N_("radiun"))/(N_("Uranium"))` in Uranium ore at equilibrium.

Explanation

In the series decay `ArarrBrarrC`, if `lambda_(A) lt lt lambda_(B)` the transient equilibrium occurs when
`(N_(B))/(N_(A))=(lambda_(A))/(lambda_(B)-lambda_(A))`. Here `A=`Uranium and `B="Radium"`
`lambda_(A)=(1)/(tau_(A))=0.693//4.5xx106 "year"^(-1)lambda_(B)=(1)/(tau_(B))=0.693//1.620 "year"`
`N("Rad")//N(U)~~1.620//4.5xx10^(9)=1//2.78xx10^(6)`