An important step in the purification of uranium isotopes involves the conversion of uranium to uranium hexafluoride, UF6. In the present process, UF6 is prepared by exposing uranium pellets, spherical in shape, to fluorine gas at 1000 K and 1 atm pressure. The molecular diffusion of the fluorine gas to the pellet surface is thought to be the controlling step. If the reaction U(s) + 3F2(g) -> UF6(g) occurs irreversibly and instantaneously on the pellet surface, and the diffusivity of fluorine gas through uranium hexafluoride gas is 0.273 cm2 /s at 1000 K and 1 atm, determine the production rate of UF6 when the pellet diameter is 0.4 cm.

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