# Atomic number density and mass density

1. Sep 13, 2013

### ulriksvensson

Hello everyone. I have a problem I can't figure out.

Let's say that we start off with UO2 fuel. Knowing the density (and enrichment) we can calculate the number densities of the constituents (i.e. U-238, U-235, U-234, O-16). Suppose now that the fuel is burned to a certain exposure. A lattice code (for instance CASMO) can calculate the mixed number densities (MND). Suppose that I wanted to check this calculation backwards - given that I know the number of oxygen atoms doesn't change it should be possible. I just can't figure out how to do it.

Does anyone know how to do it? It really would help me alot!

//Ulrik

2. Sep 17, 2013

### QuantumPion

Just divide the number density of oxygen by 2! :)

(and then multiply by the atom fraction for each uranium isotope)

3. Sep 18, 2013

### ulriksvensson

Yes I solved it the other way around:
\rho = 1/N_{a}*sum_{k=1}^{p} M_{k}*N_{k}
(Latex code)
The reason I was confues was that I forgot to compensate for thermal expansion of the fuel.