Atoms and molecules can have multiple states with different energies. They interact with their environment by exchanging energy and transitioning between different states. In this entry we discuss the hierarchy of energy between the different atomic transition. We consider three basic transition types: electronic, vibrational and rotational. The typical energy of an electronic transition $ E_e $ is of the order of magnitude of a few electron volts. The simplest example of such levels is the Bohr model for the hydrogen atom. Vibrational energy levels can be thought of as energies of a harmonic oscillator. Since the same electric forces are involved between The "spring constant" is the same as in the electronic transitions $ E_e \approx h \omega \approx h \sqrt{k/m_e} $. The mass, however, is that of the nucleus instead of the electron, so

$ E_v \approx h \sqrt{k/m_n} = E_e \sqrt{\frac{m_e}{m_n}} $

In the case of rotational energy levels, they have the same angular momentum as electronic transitions, but the rotating mass is that of the nucleus instead of the electron, therefore

$ E_r \approx E_e \frac{m_e}{m_n} $