Name: electron spin and orbital pairing
Uploaded: 2020-09-03T13:38:27.000Z
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K12 Standards

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IPC.7

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The Pauli Exclusion Principle

Atomic orbitals are the regions where an atom&#8217;s electrons are most likely to be found. But how many electrons can each orbital hold?
The Pauli exclusion principle answers this question, as it means that no two electrons in an atom can have the same set of four quantum numbers.
Every orbital corresponds to fixed principal; angular momentum, or azimuthal; and magnetic quantum number values. For example, an electron in the 1s orbital always has a principal quantum number of one and azimuthal and magnetic quantum numbers of zero.
Accordingly, electrons must have different spin quantum number values, or spins, to reside in the same atomic orbital. Recall that the spin quantum number has only two possible values: +1/2 and &#8722;1/2. Therefore, only two electrons can occupy the same orbital. 
Hence, each s subshell, which has one orbital, can accommodate only two electrons, and each p subshell, which has three orbitals, can hold six electrons. Each of the d and f subshells has a maximum capacity of ten and fourteen electrons, respectively.
The distribution of electrons among an atom&#8217;s atomic orbitals is represented by its electron configuration in text or diagram form.
Consider a ground-state hydrogen atom, where one electron occupies the lowest-energy orbital: 1s. The written electron configuration denotes each occupied subshell with the number of the corresponding shell, the letter of the subshell, and a superscript number specifying the number of electrons in the subshell.
The orbital diagram style of the electron configuration denotes each orbital within an occupied subshell as a box or line and each electron as an arrow. An upward arrow indicates a +1/2 spin, or spin-up, and a downward arrow signifies a &#8722;1/2 spin, or spin-down. The orbital diagram of hydrogen, therefore, has one upward arrow.
The electron configuration of helium is 1s2. The two electrons have three identical quantum numbers, as they belong to the same shell and subshell. Their spin quantum numbers are different, in accordance with the Pauli exclusion principle.
Electrons with opposite spins are called &#8220;paired&#8221; if they occupy the same orbital.
For lithium, which has an atomic number of three, the two electrons in the 1s orbital are paired and the electron in the 2s orbital is unpaired. Conventionally, unpaired electrons are represented as spin-up.

the pauli exclusion principle

The arrangement of electrons in the orbitals of an atom is called its electron configuration. We describe an electron configuration with a symbol that contains three pieces of information:
<ol>
	<li>The number of the principal quantum shell, n,</li>
	<li>The letter that designates the orbital type (the subshell, l), and</li>
	<li>A superscript number that designates the number of electrons in that particular subshell.</li>
</ol>
For example, the notation 2p4 indicates four electrons in a p subshell (l = 1) with a principal quantum number (n) of 2. The notation 3d 8 indicates eight electrons in the d subshell ( l = 2) of the principal shell for which n = 3.
While the three quantum numbers work well for describing electron orbitals, some experiments showed that they were not sufficient to explain all observed results. It was demonstrated in the 1920s that when hydrogen-line spectra are examined at extremely high resolution, some lines are actually not single peaks but, rather, pairs of closely spaced lines. This is the so-called fine structure of the spectrum, and it implies that there are additional small differences in energies of electrons even when they are located in the same orbital. These observations led Samuel Goudsmit and George Uhlenbeck to propose that electrons have a fourth quantum number. They called this the spin quantum number or ms.
In an applied magnetic field, an electron has two possible orientations with different energies, one with spin up, aligned with the magnetic field, and one with spin down, aligned against it.
The fourth quantum number, spin quantum number (ms) describes these two different spin states of an electron. A spin quantum number has two possible values, &#8722;1/2 (spin down) and +1/2 (spin-up).
Electron spin describes an intrinsic electron "rotation" or "spinning." Each electron acts as a tiny magnet or a tiny rotating object with angular momentum, or as a loop with an electric current, even though this rotation or current cannot be observed in terms of spatial coordinates.
The magnitude of the overall electron spin can only have one value, and an electron can only &#8220;spin&#8221; in one of two quantized states. One is termed the &#945; state, with the z component of the spin being in the positive direction of the z-axis. This corresponds to the spin quantum number ms = +1/2. The other is called the &#946; state, with the z component of the spin being negative and ms = &#8722;1/2.
Any electron, regardless of the atomic orbital it is located in, can only have one of those two values of the spin quantum number. The energies of electrons having different spins are different if an external magnetic field is applied.
An electron in an atom is completely described by four quantum numbers: n, l, ml, and ms. The first three quantum numbers define the orbital, and are interdependent, while the fourth quantum number is independent of other quantum numbers as it describes an intrinsic electron property called spin. An Austrian physicist Wolfgang Pauli (Nobel Prize in Physics: 1945) formulated a general principle that gives the last piece of information that we need to understand the general behavior of electrons in atoms. The Pauli exclusion principle can be formulated as follows: No two electrons in the same atom can have exactly the same set of all the four quantum numbers. What this means is that two electrons can share the same orbital (the same set of the quantum numbers n, l, and ml) only if their spin quantum numbers have different values. Since the spin quantum number (ms) can only have two values +1/2 and -1/2, no more than two electrons can occupy the same orbital (and if two electrons are located in the same orbital, they must have opposite spins). Therefore, any atomic orbital can be populated by only zero, one, or two electrons.
The orbital diagram style of the electron configuration represents each orbital within an occupied subshell as a box or line and each electron as an arrow. The orbital diagram of hydrogen, which an electron configuration of 1s1, is:
<img alt='Numerical symbol "1" in a square frame, graphic representation for counting or sequencing' src="/files/core/CDNSource/lessons/984/984Image_1.png" style="height: 40px;" data-altupdatedat="1761830439000" data-alt="Figure1" />
An upward arrow indicates a plus-half spin, or spin-up, and a downward arrow signifies a minus-half spin, or spin-down. The orbital diagram of hydrogen, therefore, has one upward arrow.
The electron configuration of helium is 1s2. The two electrons have three identical quantum numbers, as they belong to the same shell and subshell. Their spin quantum numbers are different, in accordance with the Pauli exclusion principle. Electrons with opposite spins are called paired if they occupy the same orbital.
<img alt="Static equilibrium diagram, symbol &#931;F=0, depicting force balance with opposing arrows." src="/files/core/CDNSource/lessons/984/984Image_2.png" style="height: 40px;" data-altupdatedat="1761830439000" data-alt="Figure2" />
This text is adapted from Openstax, Chemistry 2e, Section 6.3: Development of Quantum Theory.

The arrangement of electrons in the orbitals of an atom is called its electron configuration. We describe an electron configuration with a symbol that ...

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KEY TERMS AND CONCEPTS

electron spin and orbital pairing

Electron spin and orbital pairing explain why only two electrons can fit in one atomic orbital. Electron configuration describes how electrons are arranged in an atom’s orbitals. It is written with three parts: the principal quantum number, n, the orbital type, or subshell, and a superscript that shows how many electrons are in that subshell. For example, 2p4 means four electrons in a p subshell with n = 2, and 3d8 means eight electrons in a d subshell with n = 3.

The three quantum numbers describe orbitals well, but they do not explain every experimental result. In the 1920s, very high-resolution hydrogen spectra showed fine structure, where some lines split into two close peaks instead of one. This suggested that electrons in the same orbital can still have small energy differences. Samuel Goudsmit and George Uhlenbeck proposed a fourth quantum number to explain this behavior. They called it the spin quantum number, ms.

An electron can have two spin states in an external magnetic field. One state is spin up, which aligns with the magnetic field, and the other is spin down, which points against it. The spin quantum number has only two values, +1/2 and -1/2. These are also called the alpha and beta states. Electron spin is an intrinsic property, so each electron behaves like a tiny magnet, even though this motion cannot be observed in normal space.

A complete electron description uses four quantum numbers: n, l, ml, and ms. The first three quantum numbers define the orbital and depend on one another. The spin quantum number is independent because it describes the electron’s spin. Austrian physicist Wolfgang Pauli used this idea to state the Pauli exclusion principle. It says that no two electrons in the same atom can have the same set of all four quantum numbers.

This principle means that two electrons may share the same orbital only if their spin quantum numbers are different. Because ms has only two possible values, no more than two electrons can occupy one orbital. An atomic orbital can therefore hold zero, one, or two electrons. In orbital diagrams, each orbital is shown as a box or line and each electron as an arrow. A hydrogen atom with configuration 1s1 has one upward arrow, which means one spin-up electron.

Helium has the configuration 1s2. Its two electrons share the same shell and subshell, so they have three identical quantum numbers. They differ in spin, which follows the Pauli exclusion principle. Electrons with opposite spins in the same orbital are called paired.

Electron Spin and Orbital Pairing

the wave nature of light

Measuring Light with Wavelength and Frequency

Light can be described as an electromagnetic wave, and its behavior helps explain many patterns seen in science. For centuries, scientists have tried to understand light. Newton used lenses and prisms to show that white light is made of the colors of the rainbow mixed together. He explained light as tiny particles moving at high speed. Other scientists, including Christiaan Huygens, showed that reflection and refraction could also be explained by treating light as a wave. At the time, people...

the electromagnetic spectrum

Electromagnetic Waves: Uses Across the Spectrum

The electromagnetic spectrum includes all electromagnetic radiation arranged by frequency and wavelength. Visible light is only a small part of it, and each color of visible light has its own frequency and wavelength. Different parts of the spectrum also use different units. Radio waves are usually measured in MHz, while the visible range is often measured in nm or angstroms. The spectrum is organized from radio waves to gamma rays as frequency increases and wavelength decreases. Radio waves...

interference and diffraction

Wave Patterns from Light and Slits

Light can form wave patterns through interference and diffraction. When two electromagnetic waves meet with their peaks and troughs lined up, they combine into a larger wave. This is constructive interference, and the waves are in phase. When a peak of one wave meets a trough of the other, the waves reduce each other. This is destructive interference, and the result has a much lower amplitude. Diffraction is another wave behavior. When light passes through a slit that is about the same size as...

photoelectric effect

Why Light Ejects Electrons from Metals

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the bohr model

Bohr’s Quantized Atomic Orbits

Bohr’s quantized atomic orbits explain why hydrogen atoms can stay stable. Early in the twentieth century, Ernest Rutherford and his colleagues described atoms as tiny dense nuclei with lighter electrons moving around them. This picture was called the planetary model because it compared the atom to a miniature solar system, with electrons orbiting the nucleus like planets around the sun. The simplest atom is hydrogen. It has one proton in the nucleus and one electron moving around it. In the...

emission spectra

Line Spectra from Heated Gases

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the de broglie wavelength

Electron Waves and Standing Orbits

Electron waves and standing orbits explain how tiny particles can behave like waves. Large objects in the macroscopic world, like a billiard ball on a table, follow classical physics. A ball keeps moving in a straight line unless it hits another ball or a force such as friction acts on it. It also has a well-defined position, velocity, and momentum, where momentum is mass times velocity. Waves behave differently from macroscopic particles. When waves interact, they can form interference...

the uncertainty principle

Electron Position and Momentum Limits

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the quantum-mechanical model of an atom

Electron Orbitals in Quantum Mechanics

Quantum mechanics explains how electrons behave in atoms using waves and probability. Erwin Schrödinger built on de Broglie’s idea that an electron in hydrogen could act like a circular standing wave instead of moving in fixed circular paths. He then derived the Schrödinger equation, which became a major step in modern atomic theory. When Schrödinger applied his equation to hydrogen-like atoms, it matched Bohr’s energy expression and the Rydberg formula for hydrogen spectra. He described...

quantum numbers

Electron Orbitals and Spin

Electron orbitals are described by quantum numbers that show where an electron is most likely to be found around the nucleus. These numbers come from the quantum mechanical model, which is based on solutions of the Schrödinger equation. They also help explain why electron energy comes in set values instead of changing smoothly. The principal quantum number, n, labels the energy level. It can be 1, 2, 3, and so on, and higher n values usually mean higher electron energy. This number also tells...

atomic orbitals

Electron Regions in Atomic Orbitals

Electron regions in atomic orbitals show where an electron is most likely to be found in an atom. These three-dimensional regions are often drawn as boundary surfaces around the densest part of the cloud. The shape of an orbital depends on the angular momentum quantum number, l. This value can range from 0 to n - 1, where n is the principal quantum number. For n = 1, only l = 0 is allowed. For n = 2, both l = 0 and l = 1 are allowed. Orbitals with the same value of l form a subshell. The l =...

Electron spin and orbital pairing explain why only two electrons can fit in one atomic orbital. Electron configuration describes how electrons are arranged in an atom’s orbitals. It is written with three parts: the principal quantum number, n, the orbital type, or subshell, and a superscript that shows how many electrons are in that subshell. For example, 2p4 means four electrons in a p subshell with n = 2, and 3d8 means eight electrons in a d subshell with n = 3. The three quantum numbers...

the energies of atomic orbitals

Shielding and Orbital Penetration

Shielding and orbital penetration help explain why electrons in an atom have different energies. Electrons are attracted to the positive nucleus, but they also repel one another in atoms with more than one electron. The strength of these forces depends on the charge and the distance between the particles. Opposite charges attract, like charges repel, and the force gets weaker as the particles move farther apart. An electron that stays closer to the nucleus is held more tightly. That means...

the aufbau principle and hund's rule

Electron Filling Order in Atomic Orbitals

Electron filling order in atomic orbitals follows the aufbau principle and Hund's rule. To write an electron configuration, we build atoms in order of atomic number. Starting with hydrogen and moving across the periods of the periodic table, one proton is added to the nucleus and one electron is placed into the correct subshell. This process describes the ground-state electron configurations of the elements. The aufbau principle comes from the German word aufbau, which means "to build up." It...

electron configuration of multielectron atoms

electron-configuration-of-multielectron-atoms

Valence Electrons and Noble Gas Shorthand

Valence electrons and noble gas shorthand help show how electrons are arranged in multielectron atoms. Sodium, the alkali metal with atomic number 11, has one more electron than neon. That extra electron goes into the lowest-energy subshell available, the 3s orbital, so sodium has the configuration 1s2 2s2 2p6 3s1. Electrons in the outermost shell, where n is highest, are called valence electrons. Electrons in the inner shells are called core electrons. Because core electrons often match a...

key terms and concepts

Learn how electron spin, quantum numbers, and orbital pairing explain why each atomic orbital holds at most two electrons in high school chemistry.

Electron Spin and Orbital Pairing | JoVE K12

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NC K-12 Science Standard Course of Study

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Matter and its Interactions

PS.Chm.1.3

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Ohio’s Learning Standards and Model Curriculum

Structure And Properties Of Matter

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Matter and Its Interactions

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IPC.7.D

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New York State Science Learning Standards

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electron-configuration-and-chemical-properties

Electron Configuration and Chemical Properties

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Model basic atomic structure and relate an element's atomic structure to its bonding, reactivity, and placement on the Periodic Table.

IPC.7.A

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Physical and Chemical Properties of Matter

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Physical Properties of Matter

A physical property is ...

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Use patterns within the Periodic Table to predict the relative physical and chemical properties of elements.

IPC.7.B

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Classifying Matter by Composition

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Phase Transitions: Melting and Freezing

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Phase Transitions: Sublimation and Deposition

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IPC.7.C

Emission Spectra

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The Uncertainty Principle

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The Quantum-Mechanical Model of an Atom

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Science concepts. The student knows that relationships exist between the structure and properties of matter. The student is expected to:

Electron Spin and Orbital Pairing

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