Root mean square speed
The square root of the average of the squared speeds of gas particles: v_rms = √(3k_B T/m) = √(3RT/M) where T is absolute temperature, m is particle mass, M is molar mass, k_B is Boltzmann constant, and R is gas constant.
Formula
v_rms = √(3kBT/m) = √(3RT/M)
Real World
Uranium enrichment for nuclear fuel exploits the fact that lighter ²³⁵UF₆ molecules have a slightly higher rms speed than heavier ²³⁸UF₆, allowing separation by diffusion.
Exam Focus
Show the square root clearly in workings; examiners frequently see students omitting it and losing the final mark for an incorrect unit check.
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