Samples of two radioactive nuclides A and B are taken. λA and λB are the disintegration constants of A and B respectively. In which of the following cases, the two samples can simultaneously have the same decay rate at any time?

(a) Initial rate of decay of A is twice the initial rate of decay of B and λA = λB
(b) Initial rate of decay of A is twice the initial rate of decay of B and λA > λB
(c) Initial rate of decay of B is twice the initial rate of decay of A and λA > λB
(d) Initial rate of decay of B is same as the rate of decay of A at t = 2 h and λA < λB

1. (a, b)

2. (a, c)

3. (b, d)

4. (c, d)

(3) Hint: Decay rate depends on the no. of nuclei in a sample.
The two samples of the two radioactive nuclides A and B can simultaneously have the same decay rate at any time if initial rate of decay of A is twice the initial rate of decay of B and λA > λB. Also, when initial rate of decay of B is same as rate of decay of A at t = 2h and λA < λB.