QuestionKinetic theory / rms speed
The root mean square velocity of a monoatomic gas of molar mass ‘M’ (g mol⁻¹) is ‘u’. What is the correct relation between ‘u’ and average kinetic energy (E) per mole?
- (a) u = \(\sqrt{\frac{3E}{M}}\)
- (b) u = \(\sqrt{\frac{2E}{3M}}\)
- (c) u = \(\sqrt{\frac{2E}{M}}\)
- (d) u = \(\sqrt{\frac{E}{3M}}\)
Answer: (c) u = \(\sqrt{\frac{2E}{M}}\)
Per mole, average KE E = ½ M u² (u = rms speed, M = molar mass). So u = √(2E/M) → (c). Check: E = (3/2)RT gives u = √(3RT/M), the usual form.