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, the ratio of activity of A to B is 2:1
• D. After each has passed through 5 half-lives, ratio of activities of A to B is 64:1

Answer 1

Answer: (A), (C)

The half-lives of both the samples would be same
After each has passed through 5 half-lives, the ratio of activity of A to B is 2:1

Half life is the property of the nuclear material, an intensive property independent of the amount taken.
Half-life is used to describe a quantity undergoing exponential decay, and is constant over the lifetime of the decaying quantity. It is a characteristic unit for the exponential decay equation.
For first order decay
$N\left(t\right)=N_o{e}^{-\lambda t}$
since $\lambda$ depends on the half life it is same for both A and B
Only $N_o$ is different.
So at any given time, the ratio is equal to the initial ratio itself.