Question: Starting from the MaxwellBoltzmann distribution, eq. (18.10) for the probability of finding a particle with energy E in a gas with temperature T, show that

Starting from the Maxwell–Boltzmann distribution, eq. (18.10)

dPB VEe-E/kBT (7 kB T)3/2 dE

for the probability of finding a particle with energy E in a gas with temperature T, show that the most probable speed for a particle is v̅ = √2k_BT/m, but that the average speed of a particle is 〈v〉 = √8k_BT/πm. Verify that the most probable speed for a neutron at T = 20^◦C is ∼2200m/s.

dPB VEe-E/kBT (7 kB T)3/2 dE

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