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_(B) lt lambda_(A)`

Answer

b,d

Explanation

the two samples of the two radioactive nuclides A and B can simultaneously have the same decay rate at any time if initial of decay of A is twice the initial rate of decay of B and `lambda_(A) gt lambda_(B)`. Also when initial rate of decay of B is same as rate of decay of A at t= 2h and `lambda_(B) lt lambda_(A)`.