A sample contains 10⁻² kg each of substances A and B with half-lives 4 s and 8 s. Their atomic weights are in the ratio 1:2. After 16 s the ratio of amounts A:B is x/100. Find x.
Physics · Nuclear physics
JEE Mains 2022

Question

A sample contains 10⁻² kg each of substances A and B with half-lives 4 s and 8 s. Their atomic weights are in the ratio 1:2. After 16 s the ratio of amounts A:B is x/100. Find x.

G1 Physics · Accepted Answer

Initial numbers are proportional to mass divided by atomic mass, so the two samples contain nuclei in ratio 2:1. After 16 s, the first has undergone 4 half-lives and the second 2 half-lives. Their remaining-number ratio is [2/16]/[1/4] = 1/2. Hence x/100 = 1/2 and x = 50.