Root Mean Square Speed — the NEET Physics formula with its derivation, variables, validity constraints and worked solver.
Root Mean Square Speed Applies to ideal gases. While v rms gives a measure of the kinetic energy, it is higher than both the average speed and the most probable speed. Equate kinetic energy per mole (E k = 1/2 M v rms 2) with thermal energy from kinetic theory (E k = 3/2 RT). 1/2 M v rms 2 = 3/2 RT Multiply by 2: M v rms 2 = 3RT Divide by M: v rms 2 = 3RT/M Take square root: v rms = sqrt(3RT/M) Temperature T must be in Kelvin. Molar Mass M must be in kg/mol (often given in g/mol in chemistry contexts). Gas behaves as an Ideal Gas. Substituting Molar Mass in g/mol directly (results in 31.6x error). Confusing v rms with average velocity (v avg = sqrt(8RT/pi M)) or most probable velocity (v mp = sqrt(2RT/M)). Using Celsius for Temperature instead of Kelvin.