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The speed s ≥ 0 of a particle in a monotonic gas at equilibrium can be...

The speed s ≥ 0 of a particle in a monotonic gas at equilibrium can be approximated by the following PDF: f(s) = as2 e −bs2 where b = m 2kT , and m, k and T are respectively the mass of the particle, the Boltzmann’s constant and the temperature (in Kelvin). (a) Find a in terms of b. (b) An atom of neon has a mass of approximately 3.34 × 10−26 Kg. Given that k = 1.38 × 10−23 m2Kg/s 2K, what is the mean speed of an atom of neon in a gas at a temperature of 300 K? (c) The most likely speed is the speed at which the PDF reaches a maximum. What is the mostly likely speed for an atom of neon using the parameters given in (b)?

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