I was taught that electrons only exchange in orbitals of equal energy or degenerate orbitals. The energy of 3d orbitals is 5 and that of 4s is 4(by n+l rule), but then how is it that in the case of copper and chromium electrons exchange from 3d orbital to 4s?

  • $\begingroup$ Where do your energy numbers come from? Which unit are they in? $\endgroup$
    – Jan
    Sep 15 '16 at 9:51
  • $\begingroup$ What does "exchange" even mean... There is no promotion of electrons in Cr and Cu, that is just how their ground state is... It is not like God created all Cr atoms as 4s2 3d4 and then the Cr atoms realised "hey it makes more sense for me to exchange one 4s electron to 3d" so they moved one and are happier now. $\endgroup$
    – orthocresol
    Sep 15 '16 at 10:25

A sort of simplified answer but here goes...

Without some other excitation, electrons only "fall in" towards the nucleus. This is sort of like the fact that rocks roll down hill not up hill. So once an electron "falls in" it has excess energy that must be shed. It can either give the energy off as a photon or transfer the energy to one or more other electron(s) which then go into some excited state (Auger effect).

The transitions occur according to selection rules. If the selection rules don't allow a particular transition then it is forbidden. If the atom is in free space with no other perturbations, then forbidden transitions would not occur. However for molecules, in liquids and gases, because of vibrational and rotational microstates such a transition may actually occur but it will be relatively weak in intensity to the transitions allowed by the selection rules. Likewise forbidden transitions may occur in solids because of the vibrations of the atoms within the crystal which break the symmetry of an atom, or its excited state.

Now if an atom or molecule is excited by an external energy source, then an electron can move from a lower energy orbital to a empty higher energy orbital. Again these transitions obey the selection rules.

  • 1
    $\begingroup$ so as not to confuse/clarify, perhaps you should mention that rotational and vibrational levels only occur in molecules and don't involve electrons anyway. Breaking selection rules is usually a result of interaction by induced or external magnetic & electric fields, such as by spin-orbit coupling, Zeeman & Stark effects. Collisions can also induce transitions. $\endgroup$
    – porphyrin
    Sep 15 '16 at 7:48

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