= Hund's rules
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Allow us to determine with good approximation in a multi-electron atom which <electron configuration> have more energy. It is a bit like the <Aufbau principle>, but at a finer resolution.
Note that this is not trivial since there is no explicit solution to the <Schrödinger equation> for multi-electron atoms <Schrödinger equation solution for the hydrogen atom>[like there is for hydrogen].
For example, consider carbon which has <electron configuration> 1s2 2s2 2p2.
If we were to populate the 3 <p-orbitals> with two electrons with spins either up or down, which has more energy? E.g. of the following two:
``
m_L -1 0 1
u_ u_ __
u_ __ u_
__ ud __
``
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