Register to reply

Deriving the Bateman equation of Nuclear Decay Chains

by Elariel
Tags: bateman, chains, decay, deriving, equation, nuclear
Share this thread:
Mar13-07, 08:31 PM
P: 1
1. The problem statement, all variables and given/known data

Derive Bateman equation for a decay chain
a->b->c->d where each decays with a given mean life let decay constant be L, where L=1/mean life
Na(0)=No, Nb(0)=Nc(0)=Nd(0)=0

2. Relevant equations

Want to derive Nb(t)={(No)(La)/(Lb-La)}*{exp[-La*t]-exp[-Lb*t]}
extend for Nc(t)

3. The attempt at a solution



this is a none homogenous differential equation. I can't find a way to solve it.


I'm really not sure where to go from here.

If anyone could lend a hand it would be greatly appreciated.
Phys.Org News Partner Science news on
Security CTO to detail Android Fake ID flaw at Black Hat
Huge waves measured for first time in Arctic Ocean
Mysterious molecules in space
Mar14-07, 11:09 AM
Sci Advisor
HW Helper
P: 25,246
Ok, so what you are really asking is how to solve y'(t)+L*y(t)=f(t). You know the homogenous solution is exp(-L*t). Guess the solution will be of the form y(t)=g(t)*exp(-L*t). Put this guess into your original equation and get:


So g'(t)=exp(L*t)*f(t) and you can just integrate to get g(t).

Register to reply

Related Discussions
Bateman Equation in C++ Programming & Computer Science 5
Deriving the continuity equation from the Dirac equation (Relativistic Quantum) Advanced Physics Homework 3
Multi-decay chains Introductory Physics Homework 4
Nuclear decay Introductory Physics Homework 3
Decay Chains for Eejits High Energy, Nuclear, Particle Physics 1