Electron Configurations

Every atom has an electron configuration, which is the orbital filling of electrons in an atom based on their quantum numbers in increasing energies. A quantum number is one of four numbers, $n$, $\ell$, $m$, and $s$, that together describe the orbital state of subatomic electrons. The shell in which the electron is found is described by $n$. The subshell an electron is found in is described by $\ell=0$ for the s subshell, $\ell=1$ for the p subshell, $\ell=2$ for the d subshell, and $\ell=3$ for the f subshell. The $m$ quantum number gives the orientation of the electron. There are $2\ell+1$ possible values for any $m$. If $\ell$ is equal to 1, then $m$ can be –1, 0, or 1. The spin of the electron, $s$, is either $+1\rm{/}2$ or $-1\rm{/}2$. Hydrogen has one electron, and the quantum numbers of that electron are $n=1$, $\ell=0$, $m=0$, and $s=+1\rm{/}2$.

When writing the notation for an element, the sequence of subshells is written, with the number of electrons in each subshell identified with a superscript. Thus, for hydrogen, the notation is 1s¹. This notation is given in accordance with the Aufbau principle, which states that electrons fill orbitals in order of increasing energy. This order is given as follows:
This order can be visualized in a grid according to Madelung's rule. Thus, the electron configuration notation for bromine, which has 35 electrons, is 1s²2s²2p⁶3s²3p⁶4s²3d¹⁰4p⁵. Scientists often use an abbreviated form called the noble gas notation. This notation indicates in brackets the highest noble gas that fills the same subshells as the given element, followed by additional electrons above that noble gas. Noble gases have filled orbitals, so that part of the abbreviated form represents filled orbitals. Noble gas notation for bromine is thus [Ar]4s²3d¹⁰4p⁵. Argon is the closest noble gas before bromine on the periodic table. A degenerate orbital is one of two or more orbitals with the same energy. When filling degenerate orbitals, electrons must first singly occupy all the empty orbitals in the subshell before pairing within the same orbital, a process known as Hund's rule. Thus, electrons singly fill orbitals before they pair. The filling of orbitals can be denoted using an electron box diagram that shows the spin (up or down) of each electron in each orbital. In the orbital box diagram for oxygen, the electrons in the 2p degenerate orbital fill out as singletons before doubling up with an electron of opposite spin. The direction of the electron's spin is denoted by the direction of the arrows drawn in the orbital box diagram.