Discussion
The atomic number of an atom is 6. What is the spectroscopic notation of its ground state, according to Hund’s rules?
Answer: A
The ground state is \({}^{3}P_{0}\).
Atomic number 6 is carbon, \(1s^{2}2s^{2}2p^{2}\). Only the two 2p electrons matter. Hund's rules then fix the term:
- Maximum spin: the electrons take parallel spins, so \(S = 1\) and the multiplicity is \(2S + 1 = 3\).
- Maximum orbital angular momentum allowed with parallel spins: \(m_{l} = +1\) and \(0\), so \(L = 1\), a P term.
- The subshell is less than half filled, so the lowest level has the smallest \(J = |L - S| = 0\).
\({}^{3}P_{1}\) would apply only if \(J\) took the middle value, and \({}^{3}P_{2}\) would be the ground state for a more than half-filled shell such as oxygen. \({}^{3}D_{3}\) needs \(L = 2\), impossible for two parallel p electrons, and \({}^{3}S_{1}\) needs \(L = 0\).
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