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# Mean Free Path & surplus Uranium

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(g) Deﬁne the 'mean free path' for a neutron in a material.
Water is used as the moderator in a PWR. Calculate the mean free path of a thermal neutron in water given that the absorption cross section for thermal neutrons in water is o = 0.66 barns.
What are the consequences for the spacing of the fuel rods in a PWR?
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(h) A breeder reactor operates at a rating of 500 MW per tonne of 233U.
What other element is required for the production of 233U in the breeding process?
If the breeding ratio B = 1.16, and the reactor is run for 10 years, calculate how much surplus 233U is produced per tonne of 233U consumed assuming an energy release of 200 MeV per fission.

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#### Solution Preview

(g)
The mean free path is the average distance travelled by a moving particle between successive collisions which modify its direction or energy or other particle properties.
Mean free path,
lambda = 1/(N*sigma)
cross-section, sigma = 0.66 barns == 0.66*10^(-28) m^2
N = atomic density == molecules or atoms/volum
For water, N = density of ...

#### Solution Summary

In first question, mean free path for thermal neutrons in water is estimated. In second question, surplus uranium produced in a breeder reactor is estimated.

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