Three vessels of equal volume contain gases at the same temperature and pressure. The first vessel contains neon (monoatomic), the second contains chlorine (diatomic) and third contains uranium hexafloride (polyatomic). Arrange these on the basis of their root mean square speed (vᵣₘₛ) and choose the correct answer from the options given below:

Solution

Physics sir · 2 steps

Same temperature means same average kinetic energy, so the lightest molecule has to move fastest.

1. What decides speed. For an ideal gas, vᵣₘₛ = √(3RT/M), where M is the molar mass. All three gases are at the same temperature, so vᵣₘₛ ∝ 1/√M. Pressure and volume do not enter at all.

   vᵣₘₛ = √(3RT/M) ⇒ vᵣₘₛ ∝ 1/√M (same T)

   Gas	Molar mass M	vᵣₘₛ relative to UF₆
   Ne (mono)	≈ 20 g mol⁻¹	√(352/20) ≈ 4.2, fastest
   Cl₂ (dia)	71 g mol⁻¹	√(352/71) ≈ 2.2
   UF₆ (poly)	238 + 6 × 19 = 352 g mol⁻¹	1, slowest

2. So. Molar mass rises from neon to chlorine to uranium hexafluoride, so vᵣₘₛ(mono) > vᵣₘₛ(dia) > vᵣₘₛ(poly). That is option (b).

The idea to keep. At a fixed temperature, compare rms speeds through molar mass alone: vᵣₘₛ ∝ 1/√M. Atomicity matters only because, here, it happens to track the mass.

Answer from the NTA final answer key. Solution by PrepWiser.