The total number of degrees of freedom of a diatomic ideal gas molecule at ordinary temperatures is:

Solution

Physics sir · 4 steps

Picture a dumbbell: it can move three ways and turn two ways, and at room temperature it does not vibrate.

1. Translation. The centre of mass of the molecule can move along x, y and z. That gives 3 translational degrees of freedom.
2. Rotation. A diatomic molecule can rotate about the two axes perpendicular to the bond. Rotation about the bond axis does not count, because the moment of inertia about that axis is almost zero. That gives 2 rotational degrees of freedom.
3. Vibration. The two atoms can also vibrate along the bond. But exciting this vibration needs much more energy than kT at ordinary temperatures, so the vibration is frozen out and adds nothing.
4. So. The total is 3 + 2 = 5 degrees of freedom, which is option (b).

The idea to keep. Count translations, then rotations about axes with real moment of inertia, then ask if it is hot enough to vibrate. A diatomic gas has 5 at room temperature and 7 when vibration switches on.

Answer from the NTA final answer key. Solution by PrepWiser.