How to calculate critical atom density of a slab reactor?

[dss91]

I am given a critical bare slab reactor 150cm thick (a0=150cm) consisting of a homogenous mixture of U235 and graphite.

I am stuck on the part which asks me to calculate the critical atom dennsity. I have solved for the mass of the fuel in terms of the mass of the moderator. I would solve for the mass of the moderator by multiplying the volume of the reactor by the density of graphite and then plug that into the relation I have found for the mass of the moderator and the mass of the fuel, however since a slab reactor is defined only in width, I'm not sure how to find the volume of the reactor.

Thanks for any help.

 

[Astronuc]

Is one to assume a semi-infinite reactor. The there would be no leakage of neutrons in the lateral directions. One only needs to consider leakage in the normal direction (normal to the slab).

Criticality is usualy defined in terms of Ʃ (macroscopic cross-sections) which are simply products, Nσ.

 

[geddo]

Usually, the semi-infinite reactor parameters are calculated per unit infinite length. But i think that u should give us the problem for more help

 

[QuantumPion]

You want to solve for critical buckling, so that B^{2}_{M}=B^{2}_{G}.

B^{2}_{M}=\frac{\nu\Sigma_{f}-\Sigma_{a}}{D}

You are assuming no leakage in the lateral directions so the geometric buckling for a 1-D slab is simply:

B^{2}_{G}=(\frac{\pi}{a})^{2}

where a is the slab thickness.