The number of electrons in a neutral atom is equal to the number of protons in the nucleus, i.e., equal to the atomic number. These electrons occupy the atomic orbitals by the following three rules.
The Aufbau Principle states that electron filling follows the energy order of the orbital, starting with the lowest energy 1\(s\) orbital and progressing to higher energy orbitals. Pauli's exclusion principle states that each electron in an atom has a unique set of four quantum numbers. Since each atomic orbital has a unique set of three quantum nubmers \(n\), \(l\), and \(l_m\), it can take a maximum of two electrons: one with \(m_s = +\frac{1}{2}\), called "up spin" and represented as \(\uparrow\) or \(\upharpoonleft\) and the other with \(m_s = -\frac{1}{2}\), called "down spin" and represented as \(\downarrow\) or \(\downharpoonright\). Hund's rule states that when filling degenerate orbitals, the electrons occupy separate orbits with the same spins, usually represented as \(\uparrow\) or \(\upharpoonleft\), until no degenerate orbital is left empty. Then the additional electron pairs up with one of the singly occupied orbitals. Paired electrons and unpaired electronTwo electrons in the same orbital are called paired electrons and represented as \(\uparrow\downarrow\) or \(\upharpoonleft\downharpoonright\).
One electron in a singly occupied orbital is called an unpaired electron and is usually represented as \(\uparrow\) or \(\upharpoonleft\).
The simplest and most common way of representing an atom in a subshell is as a superscript to the shell symbol \(s\), \(p\), \(d\), or \(f\). For example, the electron configuration of hydrogen, which has one electron, is 1\(s^1\). Similarly, the electron configuration of helium with two electrons is 1\(s^2\), lithium with three electrons is 1\(s^2\) 2\(s^1\), beryllium with four electrons is 1\(s^2\) 2\(s^2\), boron with five electrons is 1\(s^2\) 2\(s^2\) 2\(p^1\), and carbon with six electrons is 1\(s^2\) 2\(s^2\) 2\(p^2\). First shell has one orbital 1\(s\) and can take two electrons, second shell with four orbitals (2\(s\) and three 2\(p\) orbitals) and can take eight electrons, third has nine orbitals (3\(s\), three of 3\(p\) and five of 3\(d\)) and can take eighteen electrons, and so on. Table 1.2.5 below shows the electron configuration of the first 18 elements.
Table 1.2.5: The electron configuration of the first eighteen elements in the periodic table (valence shells and valence electrons are shown in red fonts).Group \(\rightarrow\)
Rows \(\downarrow\)
1 2 13 14 15 16 17 18 1\(\Large_{1}\text{H}\)
\(\textcolor{red}{\text{1}s^1}\)
\(\Large_{2}\text{He}\)
\(\textcolor{red}{\text{1}s^2}\)
2\(\Large_{3}\text{Li}\)
\(\text{1}s^2\textcolor{red}{\text{2}s^1}\)
\(\Large_{4}\text{Be}\)
\(\text{1}s^2\textcolor{red}{\text{2}s^2}\)
\(\Large_{5}\text{B}\)
\(\text{1}s^2\textcolor{red}{\text{2}s^2\text{2}p^1}\)
\(\Large_{6}\text{C}\)
\(\text{1}s^2\textcolor{red}{\text{2}s^2\text{2}p^2}\)
\(\Large_{7}\text{N}\)
\(\text{1}s^2\textcolor{red}{\text{2}s^2\text{2}p^3}\)
\(\Large_{8}\text{O}\)
\(\text{1}s^2\textcolor{red}{\text{2}s^2\text{2}p^4}\)
\(\Large_{9}\text{F}\)
\(\text{1}s^2\textcolor{red}{\text{2}s^2\text{2}p^5}\)
\(\Large_{10}\text{Ne}\)
\(\text{1}s^2\textcolor{red}{\text{2}s^2\text{2}p^6}\)
3\(\Large_{11}\text{Na}\)
\(\text{1}s^2\text{2}s^2\text{2}p^6\textcolor{red}{\text{3}s^1}\)
\(\Large_{12}\text{Mg}\)
\(\text{1}s^2\text{2}s^2\text{2}p^6\textcolor{red}{\text{3}s^2}\)
\(\Large_{13}\text{Al}\)
\(\text{1}s^2\text{2}s^2\text{2}p^6\textcolor{red}{\text{3}s^2\text{3}p^1}\)
\(\Large_{14}\text{Si}\)
\(\text{1}s^2\text{2}s^2\text{2}p^6\textcolor{red}{\text{3}s^2\text{3}p^2}\)
\(\Large_{15}\text{S}\)
\(\text{1}s^2\text{2}s^2\text{2}p^6\textcolor{red}{\text{3}s^2\text{3}p^3}\)
\(\Large_{16}\text{P}\)
\(\text{1}s^2\text{2}s^2\text{2}p^6\textcolor{red}{\text{3}s^2\text{3}p^4}\)
\(\Large_{17}\text{Cl}\)
\(\text{1}s^2\text{2}s^2\text{2}p^6\textcolor{red}{\text{3}s^2\text{3}p^5}\)
\(\Large_{18}\text{Ar}\)
\(\text{1}s^2\text{2}s^2\text{2}p^6\textcolor{red}{\text{3}s^2\text{3}p^6}\)
The electron configurations shown above are simple, but when degenerate orbitals are filled, the paired and unpaired electrons are not distinguished. For example, the electron configuration of \(\ce{_{6}C}\) 1\(s^2\) 2\(s^2\) 2\(p^2\), does not show the electrons in 2\(p\) orbital are unpaired. They are unpaired based on Hund's rule. To clarify, electron configurations are shown in a box diagram with boxes representing orbitals and electrons by an up arrow for unpaired electrons and a pair of up and down arrows for paired electrons. For example, the electron configuration of \(\ce{_{6}C}\) \(\underset{1s}{\boxed{\uparrow\downarrow}}\,\underset{2s}{\boxed{\uparrow\downarrow}}\, \underset{2p}{\boxed{\;\uparrow\;}\!\boxed{\;\uparrow\;}}\); of \(\ce{_{7}N}\) \(\underset{1s}{\boxed{\uparrow\downarrow}}\,\underset{2s}{\boxed{\uparrow\downarrow}}\, \underset{2p}{\boxed{\;\uparrow\;}\!\boxed{\;\uparrow\;}\!\boxed{\;\uparrow\;}}\), and of \(\ce{_{8}O}\) \(\underset{1s}{\boxed{\uparrow\downarrow}}\,\underset{2s}{\boxed{\uparrow\downarrow}}\, \underset{2p}{\boxed{\uparrow\downarrow}\!\boxed{\;\uparrow\;}\!\boxed{\;\uparrow\;}}\).
The electrons in the outermost shell, which participate in chemical reactions, are called valence electrons, and the rest in the inner orbitals that do not directly participate in chemical reactions are called core electrons. The shell containing the valence electrons is called the valence shell, and the rest of the inner shells are called core shells.
Table 1.2.5 shows valence electrons in red and core electrons in black. If the outermost shell is \(n\), the \(ns\;np\) shell of the main group elements is a partially filled valence shell. The valence shells of noble gases are completely filled and do not usually take part in chemical reactions. A filled shell is also called a closed shell. The valence shell of transition metals is \((n-1) d\ \; ns\ \; np\). The \((n-1)d\) subshell of transition metals is partially filled and takes part in chemical reactions along with their \(ns\;np\). Similarly, the valence shell of inner transition metals is \((n-2)f\; (n-1) d \; ns\ \; np\).
Electron configuration of ionsTo write the electron configuration of an ion, first write the electron configuration of the neutral atom, then
add one electron in the outermost orbital for each negative charge for anions, or remove an electron for each positive charge in the following order: first from \(np\), then from \(ns\), then from \((n-1)d\), irrespective of their order of filling.For example
The electron configuration of \(\ce{_{6}O}\) is \(\text{1}s^2\text{2}s^2\text{2}p^4\). For anion \(\ce{_{6}O^{2-}}\) two electrons are added in the outermost orbital for 2- charge, resulting in: \(\text{1}s^2\text{2}s^2\text{2}p^6\). The electron configuration \(\ce{_{11}Na}\) is \(\text{1}s^2\text{2}s^2\text{2}p^6\text{3}s^1\). One electron is removed from \(ns\), for 1+ charge resulting in: \(\ce{_{11}Na^{+}}\) is \(\text{1}s^2\text{2}s^2\text{2}p^6\). The electron configuration of \(\ce{_{26}Fe}\) is filled in this order \(\text{1}s^2\text{2}s^2\text{2}p^6\text{3}s^2\text{3}p^6\text{4}s^2\text{3}d^6\) but usually written, as: \(\text{1}s^2\text{2}s^2\text{2}p^6\text{3}s^2\text{3}p^6\text{3}d^6\text{4}s^2\). For \(\ce{_{26}Fe^{2+}}\) two electrons are removed from the \(ns\) resulting in: \(\text{1}s^2\text{2}s^2\text{2}p^6\text{3}s^2\text{3}p^6\text{3}d^6\), and for \(\ce{_{26}Fe^{3+}}\), three electrons are removed, two from the \(ns\) and one from \((n-1)d\), resulting in: \(\text{1}s^2\text{2}s^2\text{2}p^6\text{3}s^2\text{3}p^6\text{3}d^5\). Abbreviated electron configurationThe electron configuration is abbreviated by replacing core electrons with the symbol of the noble gas hing the same electron configuration, followed by the valence shell. For example the elctron configuraiton of \(\ce{_{26}Fe}\): \(\text{1}s^2\text{2}s^2\text{2}p^6\text{3}s^2\text{3}p^6\text{3}d^6\text{4}s^2\) is abbreviated as \ce{[Ar]}\) \(\text{3}d^6\text{4}s^2\). Note that the noble gas symbol is placed in square brackets.
Figure 1.2.6 shows electron configurations of all elements. Note: there are some anomalies in the electron configuration, especially when valence \(d\) or \(f\) orbitals are near half-filled or near filled, they may draw an electron from the next \(s\) orbital to become half-filled or filled. Further details of the anomalies are beyond the scope of this book.
Figure \(\PageIndex{6}\): A periodic table of elements showing electron configurations and other properties. (Copyright; Michka B, CC BY-SA 4.0>, via Wikimedia Commons)