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At 300 K, the rms speed of oxygen molecules is √(α + 5)/α times that of its average speed in the gas. Then the value of α will be (used π = (22)/7)

Asked in JEE Main 29th Jan 2nd Shift 2023 · rms, average and most probable speed

Answer: (1) 28

Step-by-step solution

vᵣₘₛ=√(3RT)/M, average speed v=√(8RT)/(π M); the temperature and molar mass cancel in the ratio.

(vᵣₘₛ)/v=√(3π)/8.

With π=(22)/7: (3π)/8=(33)/(28).

So (α+5)/α=(33)/(28)⇒ 5α=140.

α=28.

Why the other options are wrong

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