Most Probable Speed of Gas Molecules (v_mp = √(2kBT/m) = √(2RT/M))
jee-mainjee-advanced
v_mp = √(2kBT/m) = √(2RT/M)
What each symbol means
| Symbol | What it stands for |
|---|---|
| M | Molar mass in kg/mol |
| R | Universal gas constant = 8.314 J mol⁻¹ K⁻¹ |
| T | Absolute temperature (K) |
| m | Mass of one molecule (kg) |
| kB | Boltzmann constant = 1.38 × 10⁻²³ J K⁻¹ |
| v_mp | Most probable speed — speed at peak of Maxwell-Boltzmann distribution (m/s) |
When to use this
Speed at the peak of Maxwell-Boltzmann distribution (df/dv = 0). The simplest coefficient (2) among the three speeds. Always the smallest: v_mp < v_avg < v_rms. Peak ≠ mean: most molecules have speed near v_mp, but the average is higher due to the right tail.