Consider a mixture of gas molecule of types A, B and C having masses m A < m B < m C . The ratio of their root mean square speeds at normal temperature and pressure is :

Solution

Physics sir · 4 steps

Same temperature means same average kinetic energy, so the lighter molecule has to move faster.

1. Shared temperature. In a mixture every gas is at the same temperature T. The rms speed depends only on T and the mass of one molecule.

   vᵣₘₛ = √(3kT/m) ⇒ vᵣₘₛ ∝ 1/√m

2. Order the speeds. Since m_A < m_B < m_C, the speeds run the other way: v_A > v_B > v_C. Each speed is nonzero and different, because the masses differ.
3. Flip to reciprocals. Taking reciprocals of positive numbers reverses the inequality. So 1/v_A < 1/v_B < 1/v_C.
4. So. The correct ordering is option (c).

The idea to keep. At a fixed temperature, vᵣₘₛ ∝ 1/√m: lighter means faster. When an option uses reciprocals, flip the inequality before you match it.

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