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JEE Main

Exam: JEE Main
Subject: Physics
Chapter: Kinetic Theory of Gases

JEE Main · Physics · Kinetic Theory of Gases

The rms speed of hydrogen molecule at a certain temperature is v ....

The rms speed of hydrogen molecule at a certain temperature is

v

. If the temperature is doubled and hydrogen gas dissociates into atomic hydrogen, the rms speed will become

Options

A $v$
B $\dfrac{v}{2}$
C $2v$
D $\sqrt{2}v$

Correct answer

C. $2v$

Step-by-step solution

Let the molar mass of

{H}_{2}

is

M

.

Hydrogen gas is dissociated into atomic hydrogen.

It molar mass is equal to

\dfrac{M}{2}

.

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

\dfrac{{v}_{1}}{{v}_{2}} = \sqrt{\dfrac{{T}_{1}}{{M}_{{O}_{1}}} \times \dfrac{{M}_{{O}_{2}}}{{T}_{2}}}

{T}_{2} = 2{T}_{1}and{M}_{{O}_{2}} = \dfrac{{M}_{{O}_{1}}}{2} = \dfrac{M}{2}

⇒ \dfrac{{v}_{1}}{{v}_{2}} = \sqrt{\dfrac{{T}_{1}}{M} . \dfrac{M / 2}{2{T}_{1}}} = \sqrt{\dfrac{1}{4}}

{v}_{2} = 2{v}_{1} = \text{2}v

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