# Decay chain (Bi -> Po -> Pb)

1. Dec 1, 2009

### ghetom

Hi I'm trying to do a question on nuclear decay chains. The question is:

Bi-210 decays to Po-210 by beta decay (half life = 7.2 days), and this decays by alpha decay to Pb-208 (half life = 200 decays). If A substance is initially pure Bi-210, when does the alpha emmision peak?

So far Ive got
Bi(0)=1, Po(0)=Pb(0)=o

Bi(t) = Bi(0)exp(-Lt) (L being the decay constant, t_1/2 = ln(2)/L)

and dPo(t)/dt = L(Bi(0)exp(-Lt)) -L'Po(t)

Obviously I just need to find when Po(t) is at a maximum, to find the corresponding maximum in alpha emmision, but I can't solve for Po(t)

can anyone help?

2. Dec 1, 2009

### Staff: Mentor

Well, think on mean Bi-210 => to Po-210 => Pb-206. Half-lives are 7.2 and 200 days respectively, although reliable sources indicate half-life of Po-210 is 140 d (Hyperphysics) or 138.376 d (BNL NNDC).