STANDARDPhysics-Kinetic Theory of Gases

STANDARD Physics Root Mean Square Speed MCQ Question

Type: MCQ-numerical-Medium-Class 11

A mixture of 2 moles of helium gas (atomic mass = 4 u), and 1 mole of argon gas (atomic mass = 40 u) is kept at 300 K in a container. The ratio of their rms speeds vrms (helium)vrms (argon)\frac{v_{\text{rms (helium)}}}{v_{\text{rms (argon)}}} is close to

A

2.24

B

0.32

C

0.45

D

3.16

Correct Answer

Option D

Detailed Explanation

The rms speed vrms=3RTmv_{\text{rms}} = \sqrt{\frac{3RT}{m}}. For helium, m=4m = 4 and for argon, m=40m = 40. Thus, vrms (helium)vrms (argon)=404=103.16\frac{v_{\text{rms (helium)}}}{v_{\text{rms (argon)}}} = \sqrt{\frac{40}{4}} = \sqrt{10} \approx 3.16.

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