D3.3 Orbital Energy Level Diagrams

An orbital energy level diagram (or just orbital diagram) shows the relative energies of orbitals and how electrons are distributed among orbitals within a subshell. In an orbital energy level diagram, individual orbitals are usually represented by horizontal lines whose vertical position conveys the qualitative relative energies of the orbitals. The electrons are represented as arrows with the direction of the arrow communicating the sign of ms (the ↑ arrow represents ms = +½ and the ↓ arrow represents ms = -½).

For example, a ground state boron atom has this orbital energy level diagram:

As illustrated by the boron example, an orbital diagram includes all orbitals in all subshells within a partially occupied shell, even if some orbitals are unoccupied. Note that the three 2p orbitals are degenerate, so the electron can occupy any one of them.

A carbon atom has six electrons, so there are two electrons in the 2p subshell. These two electrons could: (1) pair up in a single 2p orbital, or (2) occupy separate orbitals but with opposite spins, or (3) occupy separate orbitals but with parallel spins. All three possibilities are valid based on quantum numbers and Pauli exclusion principle, but only one is lowest in energy. Electrons having parallel spins cannot occupy the same space (the same orbital), so repulsions between them must be smaller than if they had opposite spins. Thus option 3 is lowest in energy and therefore represents the ground state of a carbon atom; options 1 and 2 represent excited states.

According to Hund’s rule, the lowest energy configuration has the maximum number of unpaired electrons with parallel spin within a set of degenerate orbitals. Thus, the orbital diagram for the ground state of carbon is

Exercise: Electron Repulsions and Unpaired Electrons


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Chemistry 109 Fall 2021 by John Moore, Jia Zhou, and Etienne Garand is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License, except where otherwise noted.