The translational degrees of freedom (fₜ) and rotational degrees of freedom (fᵣ) of CH₄ molecule are:

Solution

Physics sir · 4 steps

Methane is a 3D tetrahedron, not a line, so it can spin about all three axes.

1. Translation. Every molecule, whatever its shape, can move its centre of mass along x, y and z. So fₜ = 3 for any gas molecule.
2. Shape of methane. In CH₄ the carbon sits at the centre of a tetrahedron with four H atoms at the corners. The atoms do not lie on one line.
3. Rotation. A linear molecule has only 2 rotational degrees of freedom, because rotation about its own axis does not count. A non-linear molecule like CH₄ has a real moment of inertia about all three axes, so fᵣ = 3.
4. So. fₜ = 3 and fᵣ = 3, which is option (b).

The idea to keep. Translation is always 3. Rotation is 2 for a linear molecule and 3 for a non-linear one, so check the shape before you count.

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