Question

Two samples A and B of same radioactive nuclide are prepared. Sample A has twice the initial activity of sample B. For this situation, mark out the correct statement (s).
A. The half-lives of both the samples would be same.
B. The half-lives of the samples are different.
C. After each has passed through `5` half-lives, ratio of activity of `A` to `B` is `2:1`.
D. After each has passed through `5` half-lives, ratio of activity of `A` to` B` is `64:1`.

Answer 1

Correct Answer - a,c
Half -lives of both the samples would be same as half-life is the property of radioactive material and is independent of number of nuclei present or its activity. Let `R_(0) B =R_(0)`, then `R_(0) A=2B_(0)`, where `R_(0)` denotes initial activity.
Activity of `A` after `5` half-lives is
`R_(A) =(R_(0A))/(2^(5))=(2R_(0))/(2^(5))a`
Activity of `B` after half-lives is
`R_(B)=(R_(0B))/(2^(5))=(R_(0))/(2^(5))`
`:. (R_(A))/(R_(B))=(2)/(1)` .