Maxwell-Boltzmann Distribution

Maxwell-Boltzmann distribution: probability density of molecular speeds in a gas at thermal equilibrium.

f(v) = 4π·n·(m/(2πkT))^(3/2)·v²·exp(−mv²/2kT). Peaks at v_mp.

Tail: very few molecules at extreme speeds, but always non-zero probability.

Distribution depends only on T and m — not on V, P, or n (those just rescale).

Higher T: distribution SHIFTS RIGHT (faster speeds), BROADENS (wider spread).

Heavier gases: distribution NARROWER, lower peak speed.

Maxwell-Boltzmann is correct for CLASSICAL gases at moderate T. Quantum gases (e.g., electrons in metals) need Fermi-Dirac instead.

Underlies effusion (Graham's law), reaction kinetics (Arrhenius), evaporation, atmospheric escape.