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`?

Options

A. `6.45 yrs`
B. `4.65 yrs`
C. `5.46 yrs`
D. `5.64 yrs`

Answer

A

Explanation

`A rarr B`
At equilibrium, rate of formation of `B-` rate of decay of `B`
`:. K_(A)N_(A)=K_(B)N_(B)`
or `(K_(A))/(K_(B))=(N_(B))/(N_(A))`
or `(t_(1//2(B)))/(t_(1//2(A)))=(N_(B))/(N_(A)),` `[K=(0.693)/(t_(1//2))]`
`:. t_(1//2(B))=(1xx2xx10^(10))/(3.1xx10^(9)),[(N_(B))/(N_(A))=1:3.1xx10^(9)(given)]`
or `t_(1//2(B))=6.45 years`