(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I have solved the equation for the neutron density as a function of position and time. I need the boundary conditions to change my infinite number of solutions (the varying seperation constant) into one value so that my answer for the critical radius does not contain a sum!

2. Relevant equations

del squared (n) - A(dn/dt) = -Bn (which i have solved)

3. The attempt at a solution

i assumed spherically symmetric solutions so using spherical polar coordinates n varies only (spatially) from the distance to the centre of the sphere. The r dependence is of form cos(kr)/r + sin(kr)/r. So the coefficients of cos term must all be 0 (as the density at the centre of any given sphere cannot be infinite). I thought that at the surface, the density is 0 as neutrons do not diffuse back into the sphere once they are out. Is this right?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Deriving the critical radius of Uranium using diffusion equation

**Physics Forums | Science Articles, Homework Help, Discussion**