At radioactive equilibrium, the ratio between two atoms of radioactive elements `A` and `B` is `3.1 xx 10^(9) : 1`. If the half-life period of `A` is `2 xx 10^(10)` years, what is the half-life of `B`?

Explanation

At radioactive equilibrium `A rarr B`
`(N_(A))/(N_(B)) = (K_(B))/(K_(A)) = (t_(1//2 A))/(t_(1//2B))`
`:. (3.1 xx 10^(9))/(1) = (2 xx 10^(10))/(t_(1//2 B))` and `t_(1//2B) = 6.45` years