# How do you determine excited state electron configuration?

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Jan 26, 2016

If an electron (${e}^{-}$) configuration is not in the GROUND state, then it is in the EXCITED state.

Sodium has 11 electrons. Here are 3 possible electron configurations:

Ground state:

$1 {s}^{2} 2 {s}^{2} 2 {p}^{6} 3 {s}^{1}$: no electrons are excited from their default configuration.

Excited state "a":

$1 {s}^{2} 2 {s}^{2} 2 {p}^{6} 3 {p}^{1}$: one $3 s$ electron jumped into the $3 p$ orbital; $\text{589 nm}$ transition.

Excited state "b" (alternative to "a", but not consecutive):

$1 {s}^{2} 2 {s}^{2} 2 {p}^{6} 4 {p}^{1}$: one $3 s$ electron jumped into the $4 p$ orbital; $\text{330 nm}$ transition. (Jumping into the $3 d$ is forbidden; only $\Delta L = \pm 1$ is allowed.)

In the ground state, one would build the electron configuration by filling orbital sublevels in order from lowest to highest energy. For sodium, the ordering goes $1 s , 2 s , 2 p , 3 s , 3 p$.

(Although the next highest energy levels are $4 s$, $3 d$, and then $4 p$, a transition from the $3 s$ will not successfully go into the $3 d$ unless it goes into the $3 p$ first. It can only go to the $3 p$ or the $4 p$ in one step, if there is enough energy.)

The maximum number of electrons held by each sublevel is determined by the Pauli Exclusion Principle, ${m}_{s}$, $l$, and ${m}_{l}$:

• ${m}_{s} = \pm \text{1/2}$; therefore, one orbital, where all electrons in it have the same quantum numbers except for ${m}_{s}$, can only have two electrons, each of opposite spin ($\setminus m a t h b f \left({m}_{s}\right)$) to the other.

• $l = 0 , 1 , 2 , . . . , n - 1$ where $0 \to s$, $1 \to p$, $2 \to d$, etc. This determines the shape of the orbital.

• ${m}_{l} = 0 , \pm 1 , \pm 2 , . . . , \pm l$ determines the number of orientations an orbital can have in order to be unique and orthonormal to the others. In other words, this ultimately tells you the number of orbitals in a subshell.

To determine excited state configuration, compare it to the ground-state. Which electrons were moved to which orbitals?

Evidently, if the configurations differ, then the atom is NOT in its ground state and it must be in an excited state.

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