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Consider a mixture of gas molecules 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

Asked in JEE Main 20th July 1st Shift 2021 · Speed with temperature and molar mass

Answer: (2) 1/(v_A) < 1/(v_B) < 1/(v_C)

Step-by-step solution

At a common temperature vᵣₘₛ=√(3k_BT)/m, so v∝1/(√m).

Given m_A<m_B<m_C, the speeds run v_A>v_B>v_C.

Taking reciprocals reverses the inequality: 1/(v_A)<1/(v_B)<1/(v_C).

Why the other options are wrong

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