Consider nucleus A decaying to B with decay constant D1, B decays to either X or Y (decay constants D2 and D3). at t=0, number of nuclei of A,B,X and Y are J,J,0 and 0. and N1,N2,N3 and N4 are the number of nuclei of A,B,X and Y at any instant.
My question is, what is the relation between D1,D2 and D3 for B to first increase, peak and then decrease?
rate of decay = DN
The Attempt at a Solution
I figured the rate of accumulation of B is N1D1- N2D2- N3D3, since this also involves N, I don't know how to figure out a relation between D1,D2 and D3 alone for the specified conditions. I also figured out that no matter what D1,D2,D3 are- after a long time B will have zero nuclei (so will A).
If D1 is greater it will cause a peak but I'm not sure how the values will change with subsequent change in N