Question

Let v denote the rms speed of the molecules in an ideal diatomic gas at absolute temperature T. The mass of a molecule is ‘m’ Neglecting vibrational energy terms, the false statement is :

• A. A molecule can have a speed greater than $\sqrt{2} v$
• B. $v$ is proportional to $\sqrt{T}$
• C. The average rotational $K.E.$ of a molecule is $\frac{1}{4} m v^2$
• D. The average K.E. of a molecule is $\frac{5}{6} m \nu^2$

Answer 1

Answer: (C)

Total $K.E. = \frac{1}{2} fkT = \frac{1}{2} \left(5\right)k \left(\frac{m\nu^{2}}{3k}\right) = \frac{5}{6} m\nu^{2} $