Classical non-quantum monoatomic ideal gasses all have energy strictly equal to E=3/2 RT, fact. How will kinetic energy change if we throw in quantum mechanics?
Well nothing really, the energy equation you have there is for an ideal gas that has no real connection to the quantum level. The energy of the individual electrons is instead given by E = (h^2k/4pi.m.a^2)n^2 so unless you are confining your ideal gas to an area of about a nanometer then your 3/2 RT is a perfect indicator of the kinetic energy.
