Monoatomic Molecule

A monatomic molecule -- one made of a single atom, treated as a structureless point mass -- has no internal bonds to rotate about and nothing to vibrate against, so the only way it can store energy is by moving bodily through space. It therefore has exactly three translational degrees of freedom, one for each of the independent x, y and z directions of motion, and no rotational or vibrational degrees of freedom at all:

$f = 3.$ …