Can anyone explain Hund's rule in quantum mechanics? I asked my TA about it. She said...

Can anyone explain Hund's rule in quantum mechanics? I asked my TA about it. She said that the max spin means low energy. I dont really understand what she said. Can anyone explain it in detail?

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Expert Solution

Hund’s rules specify in a simple way that usual energy interactions dictate the ground state term

Hund's first rule states that the lowest energy atomic state is the one that maximizes the total spin quantum number for the electrons in the open sub-shell. The orbitals of the subs-hell are each occupied singly with electrons of parallel spin before double occupation occurs

Rule state that for a given electron configuration, the term with maximum multiplicity has the lowest energy. The multiplicity is equal to 2S+1.

Where ‘S’ is the total spin angular momentum for all electrons. Therefore, the term with lowest energy is also the term with maximum S. For a given multiplicity, the term with the largest value of the total orbital angular momentum quantum number has the lowest energy

As an example, consider the ground state of silicon.

The electronic configuration of Si is 1s2 2s2 2p6 3s2 3p2

Hund's first rule now states that the ground state term is 3P, which has S = 1. The superscript 3 is the value of the multiplicity = 2S + 1 = 3.

queen_honey_blossom answered 1 year ago

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