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Consider an ideal diatomic gas with molecules of mass 'm' at an absolute temperature T. Let V represent the root mean square speed of the molecules, ignoring vibrational energy contributions. Which statement is incorrect?

1. It is possible for a molecule to have a speed exceeding √2 V.
2. The value of V scales with the square root of T.
3. The mean rotational kinetic energy per molecule equals mV²/4.
4. The mean kinetic energy per molecule is 5mV²/6.

Correct answer: The mean rotational kinetic energy per molecule equals mV²/4.

Solution

With V^2 = 3kT/m, we get kT = mV^2/3. A diatomic molecule has 2 rotational degrees of freedom, so mean rotational KE = 2*(1/2)kT = kT = mV^2/3, not mV^2/4. The mean total KE = (5/2)kT = 5mV^2/6 is correct, so the incorrect statement is the rotational-KE one (mV^2/4).

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