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JEE Main 202120 JulyMorning Shift

Exam: JEE Main
Year: 2021
Date: 20 July
Shift: Morning Shift
Subject: Physics
Chapter: Kinetic Theory of Gases

JEE Main 2021 · 20 July · Morning Shift · Physics · Kinetic Theory of Gases

Consider a mixture of gas molecule of types A, B and C having...

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:

Options

A ${v}_{A} = {v}_{B} = {v}_{C} = 0$
B $\dfrac{1}{{v}_{A}} > \dfrac{1}{{v}_{B}} > \dfrac{1}{{v}_{C}}$
C ${v}_{A} = {v}_{B} \ne {v}_{C}$
D $\dfrac{1}{{v}_{A}} < \dfrac{1}{{v}_{B}} < \dfrac{1}{{v}_{C}}$

Correct answer

D. $\dfrac{1}{{v}_{A}} < \dfrac{1}{{v}_{B}} < \dfrac{1}{{v}_{C}}$

Step-by-step solution

{V}_{rms} = \sqrt{\dfrac{3RT}{M}}

{m}_{A} < {m}_{B} < {m}_{C}

⇒ {V}_{A} > {V}_{B} > {V}_{C}

⇒ \dfrac{1}{{V}_{A}} < \dfrac{1}{{V}_{B}} < \dfrac{1}{{V}_{C}}

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