# Radioactive decay A -> B -> C

1. Sep 24, 2011

### unscientific

1. The problem statement, all variables and given/known data
I learnt that radio-decay is exponential; say if A decays to B with constant y1 and B decays to C with constant y2 and C is stable, N1 is nuclei in A while N2 is nuclei in B.

N1 = N0e-y1(t)

2. Relevant equations
Then, I tried writing the decay equation for B, and hit a wall because N2 is no longer N0, as the amount originally is zero.

3. The attempt at a solution
Then i tried to derive it:
Amount = (decayed nuclei from A) + (decay of itself)

N2 = INT A1 dt + INT A2 dt

and I arrive with this crazy integration which I do not know how to solve. Are there any better ways to derive it?

2. Sep 24, 2011

### epenguin

This is the gentlest introduction to simultaneous or coupled differential equations, of which you will probably get a basinful later.

I think before anyone helps, you must actually write out the (three) equations you are trying to solve together.

But when you have done that you may see yourself how to go further and later lessons will not seem so out of the blue to you.

Last edited: Sep 24, 2011