7.3: Electron Configurations
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)- Represent the organization of electrons by an electron configuration and orbital diagram.
The flight path of a commercial airliner was once carefully regulated by the Federal Aviation Administration. Each airplane was required to maintain a distance of five miles from another plane flying at the same altitude and 2,000 feet above and below another aircraft (1,000 feet if the altitude is less than 29,000 feet). So, each aircraft only has certain positions it is allowed to maintain while it flies. As we explore quantum mechanics, we see that electrons have similar restrictions on their locations.
Electron Configurations
Can you name one thing that easily distinguishes you from the rest of the world? And we're not talking about DNA—that's a little expensive to sequence. For many people, it is their email address. Your email address allows people all over the world to contact you. It does not belong to anyone else, but serves to identify you. Electrons also have a unique set of identifiers in the quantum numbers that describe their location and spin. Chemists use an electronic configuration to represent the organization of electrons in shells and subshells in an atom. An electron configuration simply lists the shell and subshell labels, with a right superscript giving the number of electrons in that subshell. The shells and subshells are listed in the order of filling. Electrons are typically organized around an atom by starting at the lowest possible quantum numbers first, which are the shells-subshells with lower energies.
For example, an H atom has a single electron in the 1s subshell. Its electron configuration is
\[\ce{H}:\, 1s^1 \nonumber\]
He has two electrons in the 1s subshell. Its electron configuration is
\[\ce{He}:\, 1s^2 \nonumber\]
The three electrons for Li are arranged in the 1s subshell (two electrons) and the 2s subshell (one electron). The electron configuration of Li is
\[\ce{Li}:\, 1s^22s^1 \nonumber\]
Be has four electrons, two in the 1s subshell and two in the 2s subshell. Its electron configuration is
\[\ce{Be}:\, 1s^22s^2 \nonumber\]
Now that the 2s subshell is filled, electrons in larger atoms must go into the 2p subshell, which can hold a maximum of six electrons. The next six elements progressively fill up the 2p subshell:
- B: 1s22s22p1
- C: 1s22s22p2
- N: 1s22s22p3
- O: 1s22s22p4
- F: 1s22s22p5
- Ne: 1s22s22p6
Now that the 2p subshell is filled (all possible subshells in the n = 2 shell), the next electron for the next-larger atom must go into the n = 3 shell, s subshell.
Second Period Elements
Periods refer to the horizontal rows of the periodic table. Looking at a periodic table you will see that the first period contains only the elements hydrogen and helium. This is because the first principal energy level consists of only the \(s\) sublevel and so only two electrons are required in order to fill the entire principal energy level. Each time a new principal energy level begins, as with the third element lithium, a new period is started on the periodic table. As one moves across the second period, electrons are successively added. With beryllium \(\left( Z=4 \right)\), the \(2s\) sublevel is complete and the \(2p\) sublevel begins with boron \(\left( Z=5 \right)\). Since there are three \(2p\) orbitals and each orbital holds two electrons, the \(2p\) sublevel is filled after six elements. Table \(\PageIndex{1}\) shows the electron configurations of the elements in the second period.
| Element Name | Symbol | Atomic Number | Electron Configuration |
|---|---|---|---|
| Lithium | \(\ce{Li}\) | 3 | \(1s^2 2s^1\) |
| Beryllium | \(\ce{Be}\) | 4 | \(1s^2 2s^2\) |
| Boron | \(\ce{B}\) | 5 | \(1s^2 2s^2 2p^1\) |
| Carbon | \(\ce{C}\) | 6 | \(1s^2 2s^2 2p^2\) |
| Nitrogen | \(\ce{N}\) | 7 | \(1s^2 2s^2 2p^3\) |
| Oxygen | \(\ce{O}\) | 8 | \(1s^2 2s^2 2p^4\) |
| Fluorine | \(\ce{F}\) | 9 | \(1s^2 2s^2 2p^5\) |
| Neon | \(\ce{Ne}\) | 10 | \(1s^2 2s^2 2p^6\) |
Aufbau Principle
Construction of a building begins at the bottom. The foundation is laid and the building goes up step by step. You obviously cannot start with the roof since there is no place to hang it. The building goes from the lowest level to the highest level in a systematic way. In order to create ground state electron configurations for any element, it is necessary to know the way in which the atomic sublevels are organized in order of increasing energy. Figure \(\PageIndex{5}\) shows the order of increasing energy of the sublevels.
The lowest energy sublevel is always the \(1s\) sublevel, which consists of one orbital. The single electron of the hydrogen atom will occupy the \(1s\) orbital when the atom is in its ground state. As we proceed with atoms with multiple electrons, those electrons are added to the next lowest sublevel: \(2s\), \(2p\), \(3s\), and so on. The Aufbau principle states that an electron occupies orbitals in order from lowest energy to highest. The Aufbau (German: "building up, construction") principle is sometimes referred to as the "building up" principle. It is worth noting that in reality atoms are not built by adding protons and electrons one at a time, and that this method is merely an aid for us to understand the end result.
As seen in the figure above, the energies of the sublevels in different principal energy levels eventually begin to overlap. After the \(3p\) sublevel, it would seem logical that the \(3d\) sublevel should be the next lowest in energy. However, the \(4s\) sublevel is slightly lower in energy than the \(3d\) sublevel and thus fills first. Following the filling of the \(3d\) sublevel is the \(4p\), then the \(5s\) and the \(4d\). Note that the \(4f\) sublevel does not fill until just after the \(6s\) sublevel. Figure \(\PageIndex{6}\) is a useful and simple aid for keeping track of the order of fill of the atomic sublevels.
Nitrogen has 7 electrons. Write the electron configuration for nitrogen.
Solution:
Take a close look at Figure \(\PageIndex{5}\), and use it to figure out how many electrons go into each sublevel, and also the order in which the different sublevels get filled.
1. Begin by filling up the 1s sublevel. This gives 1s2. Now all of the orbitals in the red n = 1 block are filled.
- Since we used 2 electrons, there are 7 − 2 = 5 electrons left
2. Next, fill the 2s sublevel. This gives 1s22s2. Now all of the orbitals in the s sublevel of the orange n = 2 block are filled.
- Since we used another 2 electrons, there are 5 − 2 = 3 electrons left
3. Notice that we haven't filled the entire n = 2 block yet… there are still the p orbitals!
- The final 3 electrons go into the 2p sublevel. This gives 1s22s22p3
The overall electron configuration is: 1s22s22p3.
Potassium has 19 electrons. Write the electron configuration code for potassium.
Solution
This time, take a close look at Figure \(\PageIndex{5}\).
1. Begin by filling up the 1s sublevel. This gives 1s2. Now the n = 1 level is filled.
- Since we used 2 electrons, there are 19 − 2 = 17 electrons left
2. Next, fill the 2s sublevel. This gives 1s22s2
- Since we used another 2 electrons, there are 17 − 2 = 15 electrons left
3. Next, fill the 2p sublevel. This gives 1s22s22p6. Now the n = 2 level is filled.
- Since we used another 6 electrons, there are 15 − 6 = 9 electrons left
4. Next, fill the 3s sublevel. This gives 1s22s22p63s2
- Since we used another 2 electrons, there are 9 − 2 = 7 electrons left
5. Next, fill the 3p sublevel. This gives 1s22s22p63s23p6
- Since we used another 6 electrons, there are 7 − 6 = 1 electron left
Here's where we have to be careful – right after 3p6!
- Remember, 4s comes before 3d
6. The final electron goes into the 4s sublevel. This gives 1s22s22p63s23p64s1
The overall electron configuration is: 1s22s22p63s23p64s1
What is the electron configuration for Mg and Na?
- Answer Mg
- Mg: 1s22s22p63s2
- Answer Na
- Na: 1s22s22p63s1
Pauli Exclusion Principle
When we look at the orbital possibilities for a given atom, we see that there are different arrangements of electrons for each different type of atom. Since each electron must maintain its unique identity, we intuitively sense that the four quantum numbers for any given electron must not match up exactly with the four quantum numbers for any other electron in that atom.
For the hydrogen atom, there is no problem since there is only one electron in the \(\ce{H}\) atom. However, when we get to helium we see that the first three quantum numbers for the two electrons are the same: same energy level, same spherical shape. What differentiates the two helium electrons is their spin. One of the electrons has a \(+\frac{1}{2}\) spin while the other electron has a \(-\frac{1}{2}\) spin. So the two electrons in the \(1s\) orbital are each unique and distinct from one another because their spins are different. This observation leads to the Pauli exclusion principle, which states that no two electrons in an atom can have the same set of four quantum numbers. The energy of the electron is specified by the principal, angular momentum, and magnetic quantum numbers. If those three numbers are identical for two electrons, the spin numbers must be different in order for the two electrons to be differentiated from one another. The two values of the spin quantum number allow each orbital to hold two electrons. Figure \(\PageIndex{7}\) shows how the electrons are indicated in a diagram.
Vocabulary
- principal quantum number (n)
- Defines the energy level of the wave function for an electron, the size of the electron's standing wave, and the number of nodes in that wave.
- quantum numbers
- Integer numbers assigned to certain quantities in the electron wave function. Because electron standing waves must be continuous and must not "double over" on themselves, quantum numbers are restricted to integer values.
Contributions & Attributions
This page was constructed from content via the following contributor(s) and edited (topically or extensively) by the LibreTexts development team to meet platform style, presentation, and quality:
Henry Agnew (UC Davis)
Paul Flowers (University of North Carolina - Pembroke), Klaus Theopold (University of Delaware) and Richard Langley (Stephen F. Austin State University) with contributing authors. Textbook content produced by OpenStax College is licensed under a Creative Commons Attribution License 4.0 license. Download for free at http://cnx.org/contents/85abf193-2bd...a7ac8df6@9.110).