# Pauli Exclusion Principle

In 1925, the Austrian physicist Wolfgang Pauli proposed Pauli’s exclusion principle. Pauli’s exclusion principle states that no two electrons can have the same set of quantum numbers or quantum states. It is known as Pauli’s exclusion principle because it excludes electrons from being in the same quantum state. The Pauli exclusion principle is valid throughout atomic and quantum physics, it is extremely powerful and broadly applicable. Pauli’s exclusion principle is one of the important concepts that help us to understand the atomic structures and arrangement of molecules.

### What is the Pauli Exclusion Principle?

All atoms except hydrogen atoms are multi-electron atoms. The physical and chemical properties of elements are directly related to the number of electrons in a given atom. The periodic table of the elements groups elements with identical properties into columns. This systematic arrangement is related to the number of electrons in a neutral atom, known as the atomic number, denoted by Z.  The exclusion principle is key to the underlying explanations, and that it applies far beyond the realm of quantum physics.

The Pauli exclusion principle dictates this arrangement effectively forces electrons to take up space in the atom. By recognizing that no two electrons can occupy the same quantum state simultaneously, it effectively stops electrons from piling up on top of each other, thus explaining why matter occupies space exclusively for itself and does not allow other objects to pass through it, while at the same time light and radiation are allowed to pass.

The Pauli exclusion states that no two electrons can have an identical set of quantum numbers. The Pauli principle applies to identical particles with half-integral spin i.e., S = 1/2, 3/2, 5/2  In other words, each electron should have its own singlet state or unique state. The salient features of the Pauli exclusion principle are as follows:

1. In a given orbital only two electrons can occupy different quantum states.

2. The two electrons occupied in a given quantum state must have an opposite spin or in other words, should be antiparallel to one another.

The Pauli exclusion principle isn’t only valid for the electrons but also for other elementary particles with half-integral spin, for example, fermions. The Pauli exclusion principle does not hold good for the elementary particles such as bosons that possess full integer spins. The Bosons can have or share the same quantum states simultaneously, which violates the exclusion principle. Thus the Fermi Dirac distribution follows the Pauli exclusion principle whereas the Bose-Einstein distribution violates the exclusion principle.

### Define Pauli Exclusion Principle?

The Pauli Exclusion principle is one of the important principles for the arrangement of electrons in an atom along with the Aufbau principle and Hund’s rule. The Pauli exclusion principle states that- no two electrons can have the identical set of quantum numbers or quantum states simultaneously. Every electron should have a unique quantum number and quantum states.

From the Pauli exclusion principle definition, we understood that No two electrons with up spin can be arranged together at the same time no two electrons with down spin can be arranged in a single quantum state. The Pauli exclusion principle in chemistry is as important as the Pauli exclusion principle in physics.

### Pauli Exclusion Principle in Chemistry:

In chemistry, the principle is mainly used to explain or determine the electron shell structure of atoms and predict which atoms are likely to have free electrons at the end of configurations. How is the exclusion principle used in chemistry or where does it apply? So, if we have a look at the atoms whenever it gains a new electron or electrons it usually tries to reach their lowest energy state or it shifts to the outermost shell. Now, if the state has one electron then it can either be up spin or down spin. Therefore, now if we consider the Pauli exclusion principle if there are two electrons in a state, then each of the electrons must have either spin up or spin down but can not have the same spin.

### Pauli Exclusion Principle Example:

For better understanding let us have a look at an example. We can take the helium atom as a common example. The Helium atom has 2 electrons and they occupy the outermost shell with opposite spins. Here, we will see that the two electrons are in the 1s subshell where n = 1, l = 0, ml = 0 where n, l, and ml are the principal quantum number, orbital quantum number, and magnetic quantum number respectively.

Now, both electrons will have different spins. One will be ml = -1/2  and the other will be +1/2. If we plot a diagram for the distribution, then the subshell of the helium atom will be represented with one up an electron and one down electron. Therefore, 1s subshell will have two electrons, which have opposite spins.

Let us have a look at another example for the Pauli exclusion principle, if we take a hydrogen atom consisting of one electron, then it will have a 1s subshell with one up-spin electron(1s1). Moving forward, if we take up another atom such as Lithium it consists of 3 electrons, three electrons will be distributed in 2 subshells, first, two electrons will be distributed among 1s (1s2) subshell as an up-down spin pain and 2s (2s2) subshell will have a single electron with up spin. The distributions can be clearly understood if we draw the diagram as given below.

These are a few examples of how Pauli’s exclusion principle is used. Pauli’s exclusion principle plays an important role in atom physics as the arrangement of electrons is one of the important parts of the atomic structures. In advanced physics, the Pauli exclusion principle is one of the most basic observations of nature. When we try to calculate the probability of the electron in any given state, we need to write the wavefunctions. So, the particles of half-integer spin must have antisymmetric wavefunctions and particles with integer spin must have symmetric wave functions.

### Applications of Pauli Exclusion Principle:

1. No two electrons in a solid can have the same energy states. This will help us in studying the concept of Fermi levels in the band theory of solids.

2. No two electrons in an atom can have an identical quantum number, this will lead us to model the grouping in the periodic table.

3. Electron degeneracy governs the death of stars to the white dwarf stage of stars.

4. Neutron degeneracy governs the death of stars to the neutron star stage.

### Did You Know:

• The Austrian physicist Wolfgang Pauli was honored with the Nobel prize for his remarkable contribution to the field of physics. He was honored for the discovery of the exclusion principle.

• When Neil Bohr proposed his atomic theory, he conveyed that the electrons are revolving around the nucleus in a fixed orbit. After some time, the Bohr model was corrected and every electron was assigned certain quantum numbers corresponding to their distinct states and energy levels.

• Later in the early 1900s, Pauli came up with Pauli’s exclusion principle by introducing two new quantum numbers and he stated no two electrons in an atom can have the same set of quantum numbers.

• Later it was discovered that quantum numbers can also be assigned to the protons and neutrons present in an atom, and the Pauli exclusion principle is in good agreement with this.

### Electron Spin Theory

Electron spin is a quantum property of electrons and it also is a form of angular momentum. Further, the magnitude of this particular angular momentum happens to be permanent. Also, the electron spin is a fundamental property of electrons just like charge and mass. The electron spin theory explains the electron as a quantum particle. Electron Spin theory states the electron spin direction and its influence on certain properties like the magnetic properties of an atom. The electron can spin in 2 directions are Spin up and Spindown

The spin-up and spin-down directions are coordinated to the spinning in the +z or –z-direction. These are the particles that have spin 's' equal to 1/2 for electrons. The quantum theory states that the electrons are thought of like the minute magnetic bar. Its spin points to the north pole of the minute bar and if 2 proximate electrons have the same spin direction, the magnetic field formed by the electrons supports and strengthens each other. Therefore a powerful magnetic field is acquired. If the relative electrons have an opposite spin direction, the magnetic field formed by them cancels each other. Thus, no magnetic field is existent.

### Properties of Principle Quantum Numbers

• Principal Quantum Numbers represent the most likely distance between the nucleus and the electrons of an atom.

• The Principal Quantum Number's value may be any integer with a positive value that is equal to or greater than 1. The value n=1 represents that the innermost electron shell of an atom is equal to the lowest energy state, which is also called the ground state, of an electron.

• The principal quantum number can never have a negative value or be even equal to zero. This is because an atom can never have a negative value or any value for a principal shell.

• When a given electron is infused with energy which is called the excited state, the electron jumps from one principal shell to a higher shell. This causes an increase in the value of n( Principle Quantum Number). The same happens when electrons lose energy. Principal Quantum Numbers jump back into lower shells and the value of n also drops with it.

• Absorption is the process where the increase in the value of n for an electron is seen. This highlights the photons of energy being absorbed by the electron. In the same way, the decrease in the value of 'n' (Principle Quantum Numbers for an electron is called emission. In Emission, the electrons of an atom emit their energy.

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1. What is the Reason For Formulating Pauli’s Exclusion Rules?

When we look at the arrangement of electrons in an atom there are different probabilities. But electrons can not be arranged without following the basic rules. We know that the distribution of electrons is followed by the Aufbau principle and Hund’s rule. But electrons also have individual spins, thus for arranging electrons in certain orbits we need to follow Pauli’s exclusion principle.

2. What is the Difference Between Hund’s Rule and Pauli’s Exclusion Principle?

Hund’s rule gives an idea about the presence of two or more degenerate states and how the electrons can fill into them. Whereas Pauli’s exclusion principle gives an idea about what kind of electrons can be filled together.

3. What is Electronic Spin?

Electrons are the negatively charged particles in an atom and it has three intrinsic properties. The properties of electrons are mass, charge and electronic spin. The electron spin is defined as the spinning of the electron around its axis. Mathematically it can be represented as-∥S∥=$\sqrt{s(s+1)h}$ (where s is identical to a quantized spin vector, ||S|| is a spin vector, the spin quantum number (s) is the spin angular momentum, and 'is Planck's constant.)

4. What is Quantum Mechanics?

The branch of physics that involves the behavior of matter and light on a subatomic and atomic level is called Quantum Mechanics. All things follow the quantum mechanics laws, but in the case of large bodies, it’s intensely difficult to notice the quantum effects, and therefore it was explored late. Before that, the scientists had an explanation for the shells in which the electron occurs surrounding the nucleus. Quantum Mechanics is used in explaining the properties of atoms and their fundamental particles - electrons, protons, and neutrons. The properties of particles contain their relations with each other and with electromagnetic radiations.

5. What are different types of Quantum Numbers?

Quantum Numbers are the collection of numbers that are used to determine the position and energy of an electron in an atom. The 4 quantum numbers are-

• Principal Quantum Numbers- Principal quantum numbers represent the principal electron shell of an atom. These are represented by the letter ‘n’. Principal quantum numbers describe the most likely distance between the nucleus and the electrons. A larger value of the principal quantum number indicates that the distance between the electron and the nucleus is greater

• Azimuthal Quantum Numbers- The Azimuthal Quantum Numbers are also called orbital angular momentum and it says about the shape of a given orbital. It is represented by the symbol ‘l’. Azimuthal Quantum Number's value is exactly equal to the total number of angular nodes in the orbital.

• Magnetic Quantum Numbers- Magnetic Quantum Numbers describes the total number of orbitals in 1 subshell and the direction of these orbitals. Magnetic Quantum Numbers are represented by the symbol ‘ml’. The projection of the angular momentum corresponding to the orbital along a given axis is determined by magnetic Quantum Numbers.

• Spin Quantum Numbers- The Spin Quantum Numbers are liberated of the values of n, l, and ml. The value of Quantum Numbers gives an understanding of the orientation in which the electron is spinning. These are represented by the symbol ms.

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