Chemistry

The root-mean-square speed captures the "effective" speed of a gas by weighting faster molecules more heavily—it's what you get when you square each speed, average those squares, then take the square root back. Rather than just averaging the speeds directly, $v_{\text{rms}} = \sqrt{\frac{\sum v_i^2}{N}}$ tells you the speed that would give the same kinetic energy as the whole distribution. Calculate the sum of squared speeds, divide by the number of molecules, and take the square root.

The root-mean-square speed captures the "effective" speed of a gas by weighting faster molecules more heavily—it's what you get when you square each speed, average those squares, then take the square root back. Rather than just averaging the speeds directly, $v_{\text{rms}} = \sqrt{\frac{\sum v_i^2}{N}}$ tells you the speed that would give the same kinetic energy as the whole distribution. Calculate the sum of squared speeds, divide by the number of molecules, and take the square root.