In this explainer, we will learn how to use electron shell notation to identify elements and describe the electronic configurations of atoms and ions.
Quantum chemists pioneered revolutionary ideas about the structure of electrons during the 1920s. They upheaved the nuclear atomic model that had been proposed by earlier scientists like Ernest Rutherford and replaced it with more radical quantum chemical theories. Scientists like Louis de Broglie and Erwin Schrödinger showed that electrons have the properties of both waves and particles, and they proposed that atoms should be described with wave equations. Chemists now use complex mathematical functions, or atomic orbitals, to describe the location and wave-like behavior of an electron in an atom.
Definition: Atomic Orbital
Atomic orbitals are mathematical functions that describe the location and wave-like behavior of an electron in an atom.
The quantum chemists proposed four quantum numbers that can describe each different type of atomic orbital and how atomic orbitals are successively filled with electrons. The 1s atomic orbital is the lowest-energy atomic orbital. The 1s atomic orbital has a principal quantum number of one and subsidiary and magnetic quantum numbers of zero. Electrons always fill the 1s atomic orbital before they fill any other type of atomic orbital.
The principal quantum number () determines the size and extent of each electron shell. The principal quantum number can be squared to determine how many subshells there can be in any one electron shell. It can also be squared and multiplied by two to determine the maximum number of electrons that can be held in any one shell or energy level. Electron shells that have the 1, 2, 3, 4, and 5 principal quantum numbers are sometimes labeled with the X-ray spectroscopic K, L, M, N, and O letters. The P and Q letters are used for shells with principal quantum numbers 6 and 7.
|Principal Quantum Number||Shell Name||Number of Orbitals||Maximum Number of Electrons|
The periodic table does not include any one element that has an O shell () that is completely filled with electrons. Atoms tend to be extremely unstable when they have high atomic numbers. It is incredibly challenging to produce an atom that has a completely full O shell because this atom would have a very high atomic number. The atom would be extremely unstable, and it would disintegrate almost as soon as it is formed. Most chemistry textbooks focus on the first four electron shells because there are plenty of elements that have completely full K, L, M, and N shells.
The subsidiary quantum number () determines the shape of an atomic orbital. The subsidiary quantum number can be any integer between 0 and . This means that each energy shell can contain a number of subshells equal to its principal quantum number. The first electron shell () can have one subshell with a subsidiary quantum number of zero, and the second electron shell () can have two subshells with subsidiary quantum numbers of zero and one. The third electron shell () can have three subshells with subsidiary quantum numbers that range from zero to two. The fourth electron shell () can have four subshells with subsidiary quantum numbers that range from zero to three. The first four lowest -value subshells can be classified as follows.
There is a slight difference in energy between the subshells of a given energy level. The s subshell is the lowest-energy subshell, and the p subshell is the second-lowest-energy subshell. The d subshell is the third-lowest-energy subshell, and the f subshell is the fourth-lowest-energy subshell. These sentences can alternatively be expressed with the following statement: s < p < d < f.
The magnetic quantum number determines how many orbitals there are in each subshell. It also determines their orientations in space. The magnetic quantum number can be any integer that ranges from to . The s subshell has one atomic orbital, and the p and d subshells have three and five atomic orbitals. The f subshell has seven atomic orbitals. The total number of orbitals per subshell can be determined with formula.
Any one atomic orbital can only contain two electrons. This means that any one s subshell can only hold up to two electrons because s subshells have one orbital and . It also means that any one p subshell can only hold up to six electrons because p subshells have three orbitals and . This line of reasoning can be extended to determine that any one d orbital can only hold up to ten electrons.
|Value of||Subshell||Value of||Number of Orbitals||Maximum Number of Electrons in Each Subshell|
The last quantum number is the spin quantum number , and it determines the intrinsic angular momentum of an electron. Each atomic orbital can hold one spin-up-state electron and a second spin-down-state electron .
The Pauli Exclusion Principle states that no two electrons in any one atom or ion can have the same set of four quantum numbers. Every atomic orbital in any one atom will have its own set of , , and quantum numbers and every atomic orbital can hold one spin-up state electron and a second spin-down state electron .
Definition: Pauli Exclusion Principle
The Pauli exclusion principle states that no two electrons in any one atom or ion can have the same set of four quantum numbers (, , , and ).
The Pauli exclusion principle can be more easily understood if we consider the electrons of a single helium atom. The electrons of any one helium atom both occupy the same atomic orbital. They are both contained within the 1s atomic orbital. This means that they have the same principal and subsidiary quantum numbers. It also means that they have the same magnetic quantum numbers as well. The electrons both have a principal quantum number of one () and they both have a subsidiary quantum number of zero (). They both have a magnetic quantum number of zero . They cannot both have the same set of four quantum numbers, though. They must have different spin quantum numbers. They must have different spin states. This is indeed the case. One of the helium electrons stays in a spin-up state , while the other stays in a spin-down state. The helium atom electrons are in the same atomic orbital, but they obey the Pauli exclusion principle because they have different spin quantum numbers.
The aufbau principle states that the electrons of any one atom must fill the lowest-energy atomic orbitals before they can fill the other higher-energy atomic orbitals. Electrons will always fill the lowest-energy, 1s, atomic orbital and then they fill the higher-energy, 2s and 2p, atomic orbitals. The following figure shows the relative energy values of the first eighteen electron subshells.
Definition: Aufbau Principle
The Aufbau Principle states that electrons fill the lowest energy atomic orbitals before they fill higher energy atomic orbitals.
The energy-level diagram can be used to understand that electrons will always fill the 1s subshell before they start to fill the 2s subshell and that the 2p subshell will always be filled after the 2s subshell. The energy-level diagram can also be used to infer that the filling order is not straightforward. Some atomic orbitals with relatively high principal quantum numbers have to be filled before other atomic orbitals that have lower principal quantum numbers. For example, the 4s atomic orbital tends to be filled before the 3d atomic orbital because the 4s atomic orbital has the lower energy value.
The relative position of subshells on an energy-level diagram might seem confusing, but it can be understood with the relatively simple rule. The rule states that the energy of any one subshell is determined as the sum of its principal and subsidiary quantum numbers (). The following table shows the sum of the values of the seven lowest-energy orbitals. The table shows that the lowest-energy atomic orbitals have the lowest values. The 1s atomic orbital has an value of one (1), and the 2s atomic orbital has an value of two (2). This explains why the 1s and 2s atomic orbitals are filled first. The table also shows that the 4s atomic orbital has an value of four (4) and the 3d atomic orbital has an value of five (5). The 3d atomic orbital should be filled before the 4s atomic orbital because it has the lower value. This table could be extended to determine the ordering of the other types of atomic orbitals.
You will notice here that some atomic orbitals have the same value. This is not as problematic as it might seem. Quantum chemists state that we should compare principal numbers if orbitals have the same value. The higher-energy orbital will be the one that has the larger principal quantum number. The table shows that the 2p and 3s atomic orbitals both have the same value. They both have an value of three (). This does not mean they have the same energy. They have different energies because they have different principal quantum numbers. The 3s orbital has the higher energy because it has the higher principal quantum number. The 3s orbital has a principal quantum number of three, and the 2p atomic orbital has a principal quantum number of two.
Example 1: Understanding and Using the Aufbau Principle
The aufbau process determines the order in which the electronic orbitals are filled.
- Which orbital is filled after the 1s orbital?
- Which orbital is filled after the 2p orbital?
- Which orbital is filled after the 3p orbital?
The aufbau principle states that lower energy subshells are filled first and that higher energy subshells are filled second. The aufbau principle can be used together with energy-level diagrams to determine how atomic orbitals are successively filled with electrons. Subshell energy-level diagrams show that the 2s subshell has a slightly higher energy value than the 1s subshell. This suggests that the 2s subshell will be filled with electrons immediately after the 1s atomic orbital and that option A is the correct answer for the first part of this question.
Subshell energy-level diagrams show that the 3s subshell has a slightly higher energy value than the 2p subshell. This suggests that the 3s subshell will be filled with electrons immediately after the 2p atomic orbital and that option C is the correct answer for the second part of this question.
Energy-level diagrams show that the 4s subshell has a slightly higher energy value than the 3p subshell. This suggests that the 4s subshell will be filled with electrons immediately after the 3p atomic orbital and that option B is the correct answer for the third part of this question.
Hund’s rule states that electrons will singly occupy an electron subshell in one spin-up state before they start to doubly occupy a subshell in a spin-down state. This can be shown with simple schematic illustrations. The following figures represent atomic orbitals as small boxes and electrons as single-sided arrows. The spin-up-state electrons are represented as upward-facing arrows (↑), and the spin-down-state electrons are represented as downward-facing arrows (↓). The figures compare correct and incorrect electronic configurations of a nitrogen atom. It is clear that the p-orbital electrons singly occupy all of the p orbitals rather than doubly occupy one and singly occupy another.
The next figure shows the electronic configuration of an oxygen atom for the sake of completeness. The oxygen atom has four p-orbital electrons. Three of its p-orbital electrons are in the spin-up state, and the last electron is in the spin-down state. The last electron is forced to be in a spin-down state to reduce the repulsion force between the paired electrons of one of the 2p atomic orbitals.
Definition: Hund’s Rule
Hund’s rule states that electron subshells are singly occupied with spin-up-state electrons (↑) before they are doubly occupied with spin-down-state electrons (↓).
Electrons clearly resist doubly occupying a subshell if they can singly occupy it instead. This is because there are repulsion forces between the pairing electrons of any one atomic orbital. Let us consider the 2p subshell of a single nitrogen atom. The 2p subshell has a relatively low system energy if it contains three spin-up-state electrons because there are relatively weak repulsion forces between its three electrons. The 2p subshell will have higher-system energy if it contains two spin-up-state electrons and one spin-down-state electron because there will be one atomic orbital that contains two electrons. The atomic orbital will have a high system energy because it has one spin-up-state electron and one spin-down-state electron. It will have a high energy because it contains electrons that will repel each other.
One might make the incorrect assumption that oxygen could have a relatively low system energy if it had three electrons in its 2p subshell and one in its 3s subshell. This seems like a reasonable assumption because oxygen would end up having none of its 2p or 3s atomic orbitals filled with paired electrons. This seemingly reasonable assumption is entirely incorrect. The 3s subshell has a much higher energy than the 2p subshell, and an oxygen atom will end up having a very high system energy if it has one or more of its electrons in the 3s subshell. Atoms have a relatively high system energy when they have orbitals with paired electrons, but they have an even higher energy if those same electrons are placed into higher energy subshells.
Example 2: Understanding How Electrons Successively Fill Atomic Orbitals
Which diagram shows the correct placement of the first six electrons in the following graphical representation of the electronic configuration of an element?
The aufbau principle states that electrons must fill low-energy atomic orbitals before they can fill higher-energy atomic orbitals. This means that electrons will have to completely fill the lower-energy subshells 1s and 2s before they can fill the higher-energy subshell 2p. Hund’s rule states that electrons will singly occupy the atomic orbitals of a subshell before the subshell is doubly occupied. The 2p subshell would have to be filled with spin-up-state electrons before it could be filled with other spin-down state electrons. Option C does not violate these two quantum chemical rules, and we can therefore determine that it is the correct answer for this question.
We can represent full electronic configurations by writing subshell terms in consecutive order and using superscript labels to show how many electrons there are in each subshell. The following table shows the electronic configurations for elements that make up period two of the periodic table.
The baseline terms represent subshells, and the superscript terms indicate how many electrons are in those subshells. It is important to stress here that there are two common conventions for writing electronic configurations. We can appreciate the different conventions by considering the electronic configuration of krypton. The electronic configuration of krypton could be written as .
The electronic configuration of krypton could also be written as .
The first sequence is ordered in terms of position in the periodic table, and the second sequence is ordered in terms of increasing quantum numbers. We will choose to show the electronic configuration in terms of position in the periodic table here because it is more common and it seems to be easier to understand.
The electronic configuration of atoms can become quite long when we are dealing with elements that have high atomic numbers. It is sometimes easier to use bracketed noble gas terms to represent the core electrons of an element rather than include each and every single subshell term.
We can represent potassium with the electronic configuration instead of the electronic configuration. We can represent rubidium with the electronic configuration instead of the electronic configuration. We can represent cesium with the electronic configuration and francium with the  electronic configuration. The following table shows the electronic configurations of group 1 elements. The table shows both full and abbreviated electronic configurations.
|Element||Electron Configuration||Shorthand Notation|
Example 3: Identifying the Condensed Electronic configuration of a Potassium Atom
An atom of potassium has an electronic configuration of . How else can this electronic configuration be represented?
The electronic configuration of a neutrally charged atom can be written to include all of the contributing subshell terms, or it can be written much more succinctly with bracketed noble gas terms. The bracketed noble gas terms are used to represent the core electrons of an element. Potassium has the electronic configuration. Its core electrons can be represented with the noble gas term. The valence electron has to be explicitly shown if the electronic configuration is written out in full or if the electronic configuration is written with the condensed noble gas term. Option B includes both the term and the term, and we can use this information to determine that option B is the correct answer for this question.
Electrons can be removed from an atom during a chemical reaction or when the atom is being bombarded with different types of ionizing radiation. The atom of any one element will almost always lose its valence electrons before it loses any core electrons. Magnesium is a group-two metal that has the electronic configuration. Neutrally charged magnesium atoms usually lose their two 3s subshell electrons when they react with other nonmetal atoms and form ionic compounds. The magnesium atoms lose two 3s subshell electrons, and they form ions that have the electronic configuration.
Example 4: Identifying a Chemical Element from the Electronic Configuration of Its Ion
Which element is represented by and forms a ion with an electronic configuration of ?
Atoms can lose electrons either when they are reacting with other elements or when they are being bombarded with ionizing radiation. Atoms will form ions when they lose a single electron, and they will form ions when they lose two electrons. This statement suggests that the element has two more electrons than the ion. The element must have the electronic configuration because it has the electronic configuration when it loses two electrons and the 3s subshell is filled with electrons after the 2p subshell. The electronic configuration is associated with the magnesium element, and we can therefore determine that option A is the correct answer for this question.
Ionizing radiation can be used to successively displace both valence electrons and inner shell electrons from a neutrally charged atom. The first ionization energy quantifies the amount of energy that is needed to remove one mole of electrons from one mole of gaseous neutrally charged atoms and make one mole of gaseous charged ions. The first ionization energy can be described with the following general equation that uses the symbol to represent neutrally charged atoms:
The second ionization quantifies the amount of energy that is needed to make a charge state ion from a charge state ion. The third ionization energy quantifies the amount of energy that is needed to make a charge state ion from a charge state ion. The ionization energy quantifies the amount of energy that is needed to remove one electron from an atom or ion that has the charge state. The ionization energy values increase as more and more electrons are successively removed from any atom. The first ionization energy is relatively low and the second and third ionization energies are much larger.
Electrons are always removed from the outermost electron shell before they are removed from any inner electron shells. Electrons also tend to be removed from the p subshell of one energy level before they are removed from the other s and then d subshells. Krypton will lose electrons from its 4p subshell before it loses any electrons from its 4s subshell, and Rubidium will lose electrons from its 5s subshell before it loses any electrons from its 4p subshell.
Example 5: Determining Which Orbital Electrons Are Being Ionized
The 4th ionization energy of aluminum is approximately 154 eV. From which orbital is the electron being removed?
Atoms and ions can lose electrons when they are being bombarded with different types of ionizing radiation. The ionization energy quantifies the amount of energy that is needed to remove one electron from an atom or ion that has the charge state. The 4th ionization energy quantifies the amount of energy that is needed to remove one electron from a charge state ion.
Aluminum has the electronic configuration, and the aluminum ion must have the electronic configuration because outer shell valence electrons are always removed before inner shell electrons. We can state then that this 4th ionization energy describes the situation where one electron is being removed from a system that has the electronic configuration because this matches the bracketed neon noble gas term. The 4th electron must be removed from the 2p subshell because it will not come from the electron shell if it can come from the electron shell. Also, it will not come from the s subshell of the energy level if it can come from the p subshell of the energy level. This line of reasoning can be used to determine that option A has to be the correct answer for this question.
Electrons can also be excited from one atomic orbital into an altogether different atomic orbital when they absorb photons or collide with other nearby atoms or particles. The excited electron is in an unstable state, and it will ordinarily emit photons and return to its original subshell very rapidly. The electronic configuration of an excited atom is relatively easy to identify because it has an electronic configuration that does not obey the aufbau principle. Some of the high-energy electron subshells will contain at least one electron while other lower-energy electron subshells are not completely filled.
Unexcited nitrogen atoms will always have the electronic configuration, but an excited nitrogen atom could have the or electronic configuration. One of the 2p subshell electrons is excited into a 3s subshell in the first example, and one of the 2p subshell electrons is excited into the 3p subshell in the second example.
It should be clear that atoms can sometimes have the same electronic configuration as the ions of some other entirely different type of element. The neutrally charged atoms of one element can momentarily lose or gain some electrons and end up with the same number of electrons and the same electronic configuration as some other type of element. Different atom and ion systems are described as being isoelectronic when they have the same number of electrons and the same electronic configuration. The magnesium ion is isoelectronic with negatively charged fluorine ions and neutrally charged neon atoms . Each system has the or electronic configuration.
Isoelectronic systems have the same number of electrons and the same electronic configuration.
- The Pauli exclusion principle states that every electron in any one atom or ion must have its own set of four quantum numbers (, , , and ).
- The aufbau principle states that electrons fill the lowest-energy atomic orbitals before they fill any higher-energy atomic orbitals.
- Electronic configurations can be represented schematically, or they can be expressed as a series of ordered subshell terms.
- Hund’s Rule states that every atomic orbital in any given subshell is singly occupied with spin-up-state electrons (↑) before the subshell is doubly occupied with spin-down-state electrons (↓).
- The electronic configuration of a neutrally charged atom and its ions is not the same.
- The electronic configuration of an excited-state atom does not match the electronic configuration of an unexcited state atom.
- Isoelectronic systems have the same number of electrons and the same electronic configuration.