Question

1. In a given sample two isotopes A and B are initially present in the ratio of 1:2. Their half-lives are 60 years and 30 years respectively. How long will it take so that the sample has these isotopes in the ratio of 2:1?

Answer 1

After 120 years these isotopes will be in the ratio of 2:1

Explanation :

Let the initial mass of the isotopes were x and 2x

since half life of A is 60 years,

after 60 years isotope A will become----> x/2

since half life of B is 30 years,

after 60 years isotope B will become----> 2x/4 = x/2

Again After 60 years more,

isotope A will become----> (x/2)/2 = x/4

isotope B will become-----> (x/2)/4 = x/8

Ratio of mass of A and B = (x/4) : (x/8) = 2 : 1

Hence after 120 years these isotopes will be in the ratio of 2:1