Passage II (Questions 1-7)

    Nuclear reactors requiring uranium use the isotope ²³⁵U as the fuel. Naturally occurring uranium is only 0.72% ²³⁵U, with the majority of the uranium being the ²³⁸U isotope. For a reactor to run efficiently, the uranium should be at least 3% ²³⁵U. To enrich the sample with ²³⁵U, the uranium is converted to the hexafluoro species (UF₆), a white solid at room temperature. The uranium hexafluoride compound is heated to its vaporization point and the gas is allowed to effuse through tiny pores between a series of connected containers. With each effusion, the vapor becomes enriched with the ²³⁵U species, because the lighter compound will effuse faster according to Graham's Law. The relative rates of ²³⁵UF₆ and ²³⁸UF₆ are determined below:




    Because the velocity of the U-235 species is 0.4% greater, the effusion rate of the U-235 species will be 0.4% faster. This is assuming that the diameters of the ²³⁵UF₆ and ²³⁸UF₆ molecules are equivalent. This is a valid assumption because the only difference between the two isotopes of uranium is three neutrons. Only electrons affect the radius of an atom. By carrying out successive effusions, the uranium can be enriched up to the necessary 3%. Once this is complete, the UF₆ is converted back to uranium metal.