If the root mean square velocity of hydrogen molecule at a given temperature and pressure is $2 \mathrm{~km} / \mathrm{s}$, the root mean square velocity of oxygen at the same condition in $\mathrm{km} / \mathrm{s}$ is :

JEE Main · 2024 · 01 Feb 2024 · Shift 2 · Heat & Thermodynamics

If the root mean square velocity of hydrogen molecule at a given temperature and pressure is

2 km / s

, the root mean square velocity of oxygen at the same condition in

km / s

is :

(A)2.0
(B)0.5✓ Correct
(C)1.5
(D)1.0

Answer: (B)

Solution

At the same temperature,

v_{r m s} = \frac{3 R T}{M}

, so for two gases at equal temperature the ratio of rms speeds is

\frac{v _{1}}{v _{2}} = \frac{M _{2}}{M _{1}}

. For hydrogen (

M_{1} = 2

) and oxygen (

M_{2} = 32

\frac{2}{v _{2}} = \frac{32}{2} = 4

, giving

v_{2} = 0.5

km/s.

JEE Main · 2024 · 01 Feb 2024 · Shift 2 · Single correct option

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