At radioactive equilibrium, the ratio of two atoms A and B are 3.1 × 109 = 1. If half life of A is 2 × 1010 years, then what is the half life of B?

A→BAt equilibrium, rate of formation of B = rate of decay of B∴KANA=KBNBor KAKB=NBNAt1/2(B)t1/2(A)=NBNA K=0.693t1/2∴t1/2(B)=1×2×10103.1×109; NBNA=1:3.1×109( given ) or t1/2(B)=6.45 years