Radioactive isotopes X and Y have half lifes of 4 days and 16 days respectively. The total activity of their mixture is 1 curie at certain time. The activity reduces by 50% in 8 days. Determine the ra

Question

Radioactive isotopes X and Y have half lifes of 4 days and 16 days respectively. The total activity of their mixture is 1 curie at certain time. The activity reduces by 50% in 8 days. Determine the ratio ( N x ​ / N y ​ ) of their initial number of atoms.

TestHub · Accepted Answer

Let a = λ X ​ N X ​ and b = λ Y ​ N Y ​ (initial activities). Then: a + b = 1 After 8 days (2 half-lives of X, half of Y): 4 a ​ + 2 ​ b ​ = 2 1 ​ a ≈ 0.453 , b ≈ 0.547 N Y ​ N X ​ ​ = b / λ Y ​ a / λ X ​ ​ = b a ​ × T Y ​ T X ​ ​ = 0.547 0.453 ​ × 16 4 ​ ≈ 0.207 = 2 2 ​ − 1 ​ Hence option (B).

Physics - Modern Physics Question with Solution | TestHub

Options:

Doubts & Discussion