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In a certain particle accelerator, protons travel around a circular path of diameter D in an evacuated chamber, whose residual gas is at temperature T and pressure p. Assuming T is given in Kelvin and p in pascals, calculate the number n of gas molecules per cubic meter under these conditions. What is the mean free path of the gas molecules if the molecular diameter is d. State your answers in terms of the given variables, using the Boltzmann constant k and ? if necessary.

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