The root mean square velocity of one mole of a monoatomic gas having molar mass $M$ is ${u}_{{r} . {m} . {s}}$. The relation between the average kinetic energy ($E$) of the gas and $u_{ {r.m.s. }}$ is

$u_{ {r.m.s. }}=\sqrt{\frac{3 E}{2 M}}$

$u_{ {r.m.s. }}=\sqrt{\frac{2 E}{3 M}}$

$u_{ {r.m.s. }}=\sqrt{\frac{E}{3 M}}$

JEE CHEMISTRY MCQ: STATES OF MATTER

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The root mean square velocity of one mole of a monoatomic gas having molar mass

M

{u}_{{r} . {m} . {s}}

. The relation between the average kinetic energy (

E

) of the gas and

u_{ {r.m.s. }}

View answer and explanation

Correct option: C

u_{ {r.m.s. }}=\sqrt{\frac{2 E}{M}}

Option C (

u_{ {r.m.s. }}=\sqrt{\frac{2 E}{M}}

) is correct because the root mean square velocity is related to the average kinetic energy by the formula E = (1/2) * M * u_rms².

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