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The relation between root mean square speed (vᵣms) and most probable speed (vₚ) for the molar mass M of oxygen gas molecule at the temperature of 300 K will be

Asked in JEE Main 25th June 1st Shift 2022 · rms, average and most probable speed

• (1) vᵣms = √2/3 vₚ
• (2) vᵣms = √3/2 vₚ
• (3) vᵣms=vₚ
• (4) vᵣms = √1/3 vₚ

Step-by-step solution

Why the other options are wrong

• (1) The inverted ratio: vᵣₘₛ is the larger of the two, so the factor must exceed 1.
• (3) The two are not equal; the Maxwell distribution is skewed, so its peak sits below the rms value.
• (4) Comes from comparing vᵣₘₛ with √(RT)/M rather than with the most probable speed.

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