Natural uranium ore consists mostly of the isotope U-238 (92 protons and 146 neutrons), but 0.7% of the ore consists of the
isotope U-235 (92 protons and 143 neutrons). Because only U-235 fissions in a reactor, industrial processes are used to
enrich the uranium by enhancing the U-235 content.
One of the enrichment methods is “gaseous diffusion.” The gas UF6, uranium hexafluoride, is manufactured from supplies
of natural uranium and fluorine (each of the six fluorine atoms has 9 protons and 10 neutrons). A container is filled with
UF6 gas. There are tiny holes in the container, and gas molecules leak through these holes into an adjoining container,
where pumps sweep out the leaked gas.
(a) Explain why the gas that initially leaks into the second container has a slightly higher fraction of U-235 than is
found in natural uranium.
(b) Estimate roughly the practical change in the concentration of U-235 that can be achieved in this single-stage
separation process. Explain what approximations or simplifying assumptions you have made to obtain your estimate.
(c) A typical nuclear reactor requires uranium that has been enriched to the point where about 3% of the uranium is U235. Estimate roughly the number of stages of gaseous diffusion required (that is, the number of times the gas must
be allowed to leak from one container into another). Note that the effects are multiplicative.
This is why a practical gaseous diffusion plant has a large number of stages, each operating at high pressure, which makes
this an expensive process. The first large gaseous diffusion plant was constructed during World War II at Oak Ridge,
Tennessee, and used inexpensive Tennessee Valley Authority electricity.