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

G1 Physics · Accepted Answer

For a gas, v(rms) = √(3RT/M) and v(avg) = √(8RT/(πM)). Hence [v(rms)/v(avg)]² = 3π/8. Given this equals (α+5)/α. Thus 3π/8 = (α+5)/α. Using π = 22/7 gives α = 28.