Which type of molecular motion does contribute towards internal energy for an ideal mono-atomic gas?
U=f2N k T where f = number of degrees of freedom
In an ideal mono-atomic gas, the internal energy is contributed only due to the translational kinetic energy.
For example if we take He or Ne, the atoms are not bound to each other and hence they do not vibrate. Rotational energy is neglected since their atomic moment of inertia is minimal and higher energy excitation electronically also is not possible (except at very high temperatures).
Thus, the internal energy changes in an ideal mono atomic gas are purely translational and there are 3 degrees of freedom. In other words translation can take place in 3D space i.e. x, y and z directions.
If there are N atoms in the gas, the total energy U is given by
U=32N k T