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RMS speed
Intermediate
Root-mean-square molecular speed.
v_rms = √(3k_BT/m)v_rms = √(3kT/m) = √(3RT/M). Lighter molecules move faster at the same temperature.
Nitrogen at 300 K: 517 m/s; hydrogen: 1930 m/s.
Not the same as the average speed.
In more detail
The root-mean-square speed of gas molecules is v_rms = sqrt(3kT/m). It is a convenient measure of typical molecular speed.
Real-world uses
- Estimating how fast hydrogen molecules move at room temperature.
- Predicting diffusion rates of gases.
- Chemists estimate how fast hydrogen molecules move at room temperature, which is over a kilometre per second.
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Frequently asked questions
Why is rms used?
Because it relates directly to kinetic energy, making calculations simple.
Do lighter molecules move faster?
Yes, at the same temperature, lighter molecules have higher rms speeds.
Is rms speed the same as average speed?
No. The rms speed is slightly larger than the average speed, because squaring weights the faster molecules more.
Related topics in Kinetic Theory & Statistical Physics
Pressure from molecular collisions · Kinetic interpretation of temperature · Boltzmann constant · Mean free path · Collision frequency · Degrees of freedom