Question

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

Let say initially A present = x

Then B present = 2x

Let say after 60y years the

A: B = 2:1

A after 60y years = A / 2^(60y/60)

= x/2^y

B after 60y years = B/ 2^(60y/30)

= 2x/ 2^2y

A/B = 2/1 after 60 years

A = 2B

x/2^y = 2 × 2x/ 2^2y

2^2y/2^y = 4

2^y = 2^2

y =2

After 60y = 60*2 = 120 years