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

Question

At 300 K , the rms speed of oxygen molecules is α + 5 α times to that of its average speed in the gas. Then, the value of α will be (use π = 22 7 ), 32, 28, 24, 27

MARKS App · Accepted Answer

RMS speed is given by, v r m s = 3 R T M and average speed is given by, v a v g = 8 π R T M . As per question, v r m s = α + 5 α v a v g ⇒ 3 R T M = α + 5 α 8 π R T M ⇒ 3 = α + 5 α × 8 22 7 ⇒ α = 28

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