Sample of two radioactive nuclides `A` and `B` are taken. `lambda_(A)` and `lambda_(B)` are the disintergration constants of `A` and `B` respectively. In which of the following cases, the two sample can simultaneously have the same decay rate at any time ?

Options

A. Initial rate of decay of A is twice the initial rate of decay of B and `lambda_(A) = lambda_(B)`
B. Initial rate of decay of A is twice the initial rate of decay of B and`lambda_(A) gt lambda_(B)`
C. Initial rate of decay of B is twice the initial rate of decay of A and `lambda_(A) gt lambda_(B)`
D. Initial rate of decay of B is same as the rate of decay of A at t = 2h and`lambda_(A) lt lambda_(B)`.

Explanation

The two samples can simultaneously have the same decay rate, if initial rate of decay of A is twice the initial rate of decay of B and`lambda_(A) gt lambda_(B)`. This is because rate of decay is equal to `lambdaN`. So at some point, this product for the two samples will become equal. Similar is the case when initial rate of decay of B is same as the rate of A at t = h and `lambda_(B) lt lambda_(A)`. . This can be shown by the graph for better understanding. The correct options are (b) and (d).