Only so many electrons can fit in one part of an atom before it becomes overfilled. As a result, the arrangement of electrons in atoms tend to follow a pattern, which is written out with electron configurations.
However, there are some necessary fundamentals that must be understood about how electrons align before you can learn to write out electron configurations.
Energy levels are the “groups” in which electrons align themselves into, beginning with the first energy level, which is located closest to the positively-charged nucleus, and then up from there. The table below shows how many electrons can fit into each energy level:
Sublevels are subgroups within the energy level, and are classified by the energy level and the shape of its orbital. An orbital is a ring of some shape that holds two electrons. Some types of orbitals are present in multiples in each energy level, and some sublevels don’t exist within certain energy levels because of a lack of space. Below is a table that displays what sublevels are available for each energy level. Any sublevel that is present in an energy level will always be present for all subsequent energy levels.
A fundamental theorem of sublevels to be familiar with is known as Pauli’s Exclusion Principle. This rule states that a sublevel will only contain two electrons at most, and if there are two, the spin of the electrons (their rotational directions) will be opposite.
Example 1: A particular orbital (it doesn’t matter what kind) has one electron in it. We know the following about the orbital:
It can accept one more electron, which would have an opposite spin of the electron already present. Chemical reactions can cause the electron present to be removed, resulting in an empty orbital.
There are five types of sublevels, each with a different shape. They are always filled in the same order in each energy level. These sublevels are listed in that order.
s- sphere
p- figure eight
d- dumbbell
f- irregular
g- irregular
The following sublevels exist based on space in the atom and are filled in this order: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f, 6d, 7p
It is expected that more exist, but no known atoms need to fill any electrons beyond the 7p sublevel.
In an atom, there are a certain number of orbitals for each type of sublevel.
| Sublevel Type | Relevant Energy Levels | # orbitals/energy level |
|---|---|---|
| s | 1, 2, 3, 4, 5, 6, 7 | 1 |
| p | 2, 3, 4, 5, 6, 7 | 3 |
| d | 3, 4, 5, 6, 7 | 5 |
| f | 4, 5, 6, 7 | 7 |
| g | 5, 6, 7 | 9 |
An electron configuration can be found in one of two forms: ground state or excited state. The ground state is the "default" electron configuration when none of the electrons are being affected by sources of energy outside the atom. Whenever one or more electrons in the atom are being affected in such a way, the electron configuration is in the excited state. Once the method of writing out electron configurations is introduced (next section), you will be able to tell whether the electrons are in the ground state or excited state.
Example 2: A helium atom has two electrons. A helium atom in the ground state will have two electrons in the 1s orbital, since it is the lowest energy and according to Pauli's Exclusion Principle, there is room for both electrons there, and they will have opposite spin directions. If the atom is in excited state, at least one electron will be found in another orbital.
Now we can learn to write electron configurations by hand. The notation is based on in which orbitals/sublevels the electrons are located.
The electron configuration will be written with the electrons in the order of the sublevels in increasing energy (it is unconventional to show specific orbitals in electron configurations). As a final note, feel free to use a periodic table while doing these, especially for transition metals.
Example 3: Write the ground-state electron configuration for Nitrogen.
Solution: Oxygen atoms have 8 electrons. We write out the location of electrons starting with the lowest energy level. The exponents refer to how many electrons are in the sub level; thus the
$$1s^2$$
This sublevel is filled, so we move into the next one:
$$1s^22s^2$$
The next sublevel, \(2p\), has room for 6 electrons, but only four electrons are left in the atom, so we just fill up the sublevel as much as possible:
$$1s^22s^22p^4$$
Note that this is for an oxygen atom in the ground state; excited state electrons add a layer of complication to this procedure.
Here is another example; this procedure takes some practice.
Example 4: Write the ground-state electron configuration for Calcium.
Solution: Again we go through the sublevels one at a time.
$$1s^2$$ $$1s^22s^2$$ $$1s^22s^22p^6$$ $$1s^22s^22p^63s^2$$ $$1s^22s^22p^63s^23p^6$$ $$1s^22s^22p^63s^23p^64s^2$$
Here is one final example, involving a transition metal.
Example 5: Write the ground-state electron configuration for a Tungsten atom.
Solution: There are 74 electrons, so the writing process will be more time-consuming this time. We will go one energy level at a time.
$$1s^2$$ $$1s^22s^22p^6$$ $$1s^22s^22p^63s^23p^6$$ $$1s^22s^22p^63s^23p^64s^23d^{10}4p^6$$ $$1s^22s^22p^63s^23p^64s^23d^{10}4p^65s^24d^{10}5p^6$$ $$1s^22s^22p^63s^23p^64s^23d^{10}4p^65s^24d^{10}5p^66s^24f^{14}5d^4$$
As explained earlier, electrons in the excited state violate these principles. So really, any electron configuration that is not ground state is excited state.
Example 6: The ground state electron configuration for Helium is \(1s^2\). However, in excited state at least one of the two electrons will be "out of place" and located in a different sublevel. Here are three possible excited state electron configurations for Helium atoms:
$$1s^12s^1$$ $$2s^2$$ $$2s^14f^1$$
Note the last one is not very realistic, but in theory still possible. It takes a lot of energy to move an electron through that many energy levels.
Here is another slightly different example:
Example 7: Below is an electron configuration for Titanium:
$$1s^22s^22p^63s^23p^64s^23d^2$$
Is this a ground state electron configuration or an excited state electron configuration?
Solution: Each consecutive sublevel is filled before electrons begin to fill the next one. Therefore this is a ground state electron configuration.
Note that an electron configuration only deals with the electrons in an atom, not protons or neutrons. Therefore the electron configurations for ions can be written in the same way, once the number of electrons are known.
Example 8: The isoelectronic series is the set of atoms/ions with exactly ten electrons; the ground state electron configuration for each member of the isoelectronic series is the same. To figure out what that is, realize that Neon atoms have 10 electrons, and we can build that electron configuration with ease:
$$1s^22s^22p^6$$
Therefore all atoms/ions with exactly 10 electrons, all in the ground state, have this electron configuration. This includes these common ions:
$$C^{4-}$$ $$N^{3-}$$ $$O^{2-}$$ $$F^{-}$$ $$Na^{+}$$ $$Mg^{2+}$$ $$Al^{3+}$$
Here is another example involving the electron configuration of ions.
Example 9: Write the electron configuration for a ground state \(Br^{-}\) ion.
Solution: A Bromide ion with a -1 charge has one more electron than a Bromine atom, so its electron configuration will resemble the stable Krypton atom. We can then treat the ion as a Krypton atom to write the electron configuration:
$$1s^22s^22p^63s^23p^64s^23d^{10}4p^6$$
Some elements are too painstaking to write standard electron configurations for. There is a shortcut for this, known as noble gas notation. The shortcut bases the abbreviation on the noble gas that has the most electrons but less than the number in the atom/ion you are working with. That noble gas's atomic symbol is placed in brackets to stand for the ground state electron configuration of that noble gas. Then you write out the rest like a standard ground state electron configuration.
Example 10: The regular ground state electron configuration for sodium atoms is
$$1s^22s^22p^63s^1$$
However, the last noble gas before sodium, neon, has this electron configuration:
$$1s^22s^22p^6$$
Therefore we can write this noble gas notation for the sodium atom:
$$[Ne]3s^1$$
Example 11: Write a noble gas notation for an Indium atom with all electrons in the ground state.
Solution: The last noble gas before Indium is Krypton, so the noble gas notation for Indium will be based on the electron configuration for Krypton:
$$[Kr]$$
We then fill out the rest like a regular electron configuration, starting with the electrons that fill the \(5s\) sublevel:
$$[Kr]5s^24d^{10}5p^1$$
As a check, the regular ground state electron configuration for Indium atoms is
$$1s^22s^22p^63s^23p^64s^23d^{10}4p^65s^24d^{10}5p^1$$
Noble gas notations work for ions as well. Here is one example to illustrate that.
Example 12: Write the noble gas notation for a \(Ca^{2+}\) ion.
Solution: The regular electron configuration will be the same as that of a Argon atom since the two have the same number of electrons, so we must start at the last noble gas before Argon, which is Neon.
$$[Ne]$$ $$[Ne]3s^23p^6$$
This article should have made you familiar not only with writing electron configurations, but why they are relevant to the structure of atoms in general. This topic is a building block of other topics in chemistry as well.