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At 300 K, the rms speed of oxygen molecules is sqrt((alpha + 5) / alpha) times the average speed. Find the value of alpha. (Use pi = 22/7.)

1. 25
2. 26
3. 27
4. 28

Correct answer: 28

Solution

For an ideal gas: v_rms = sqrt(3RT/M) and v_avg = sqrt(8RT/(pi*M)). Their ratio: v_rms/v_avg = sqrt(3*pi/8). Given ratio = sqrt((alpha+5)/alpha). Equating: (alpha+5)/alpha = 3*pi/8. With pi = 22/7: 3*(22/7)/8 = 66/56 = 33/28. So (alpha+5)/alpha = 33/28 → 28*(alpha+5) = 33*alpha → 28*alpha + 140 = 33*alpha → 5*alpha = 140 → alpha = 28.

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