Is Internal Energy = (3/2)nRT for a ideal monoatomic gas?
Molecules have internal energy due to intermolecular interactions, as well as translational kinetic energy, rotational energy, vibrational energy, electronic energy (and if you care to include them, nuclear energy and the mass-energy of the protons, neutrons and electrons themselves).  

By saying "ideal", energy due to intermolecular interactions is eliminated.  

By saying "monoatomic", energy due to rotation and vibration is eliminated.  

So only translational kinetic energy and electronic energy remains.  

(3/2)nRT is the translational kinetic energy, and since almost all atoms are in the ground electronic state at low temperature, it is a good expression for internal energy as long as the temperature is low enough that essentially all atoms are in the electronic ground state.