Quantum Numbers - Defintion and Types | Turito (2023)

Quantum Numbers

An atom can consist of a large number of orbitals. Based on the quantity, these orbitals can be differentiated by their shape, size, and direction of the electron or their spin, i.e., orientation.

The smaller the size of an orbital, the more the chances of finding the electrons near the nucleus. Likewise, the shape and orientation of an atom inform the probability of locating the electron in a fixed direction more than others. Atomic orbitals are accurately distinguished by some numbers, which are called quantum numbers.

This article will inform you about quantum numbers and how to calculate them.

Quantum Numbers and Their Types

Quantum numbers are the integral numbers used to describe the precise information of an electron in an atom. Simply put, quantum numbers are used to explain the correct address of an electron.

A quantum number narrates

  • The energy of an electron in orbit.
  • The position or distance of an electron from the nucleus.
  • The shape and number of orientations of an electron cloud around its axis.
  • The direction of the spinning of the electron around its axis.

These are the four quantum numbers, i.e., principal quantum number (n), magnetic quantum number (m), azimuthal quantum number (l), and spin quantum number (s). Therefore, it can say that to describe an electron in an atom completely, four quantum numbers are required.

(Video) Quantum Numbers, Atomic Orbitals, and Electron Configurations

Principal Quantum Number (n)

The principal quantum number gives the following information:

  • It determines the energy of an electron and the average distance of an electron from the nucleus. The principal quantum number tells the principal energy level of the electron. It can have any whole number value such as 1, 2, 3, 4, etc.
  • The energy levels or shells corresponding to these numbers are designated as K, L, M, N, etc. As the value of n increases, the electron gets farther from the nucleus, increasing its energy. The higher the value of n, the higher the electronic energy of the electron. Therefore, it is less tightly held with the nucleus.
  • The energy of the electron in a hydrogen atom is related to the principal quantum number by the following relation:

Eₙ = – k² [2𝜋²me⁴Z²] / [n² h²]

Where m = mass of an electron

e = charge on electron

h = Planck’s Constant

Eₙ = energy of the electron in nth principle shell in Joule

(Video) Quantum Number | Principle Quantum Number | Azimuthal | Magnetic and Spin Quantum Number

n = Principal quantum number used to designate the principal shell

k = Coulomb’s law constant

This relation is similar to the expression given by Bohr.

The principal quantum number, n, also gives the maximum number of electrons that may accommodate a given shell. The maximum number of electrons in the nth shell = 2n².

Azimuthal Quantum Number (l)

This quantum number is also called the angular quantum number. It decides the angular momentum of an electron and is denoted by l. The value of l gives the sublevel or subshell in which the electron is located.

This quantum number also decides the shape of the orbital in which the electron is located. The number of subshells with a principal shell is determined by the value of n for that principal energy level. Therefore, l may have all possible whole number values from 0 to (n – 1) for each principal energy level.

(Video) Orbitals, Atomic Energy Levels, & Sublevels Explained - Basic Introduction to Quantum Numbers

This quantum number directs the magnitude of the orbital angular momentum. Therefore, it is also called orbital angular momentum quantum number. The maximum number of electrons that may accommodate a given subshell equals 2(2l + 1).

Azimuthal quantum number rules:

  • For n = 1, l will be 0. It means that an electron in the first energy level can be present only in an s -shell. So, the first energy level has solely one subshell, i.e., 1s. It is spherical.
  • For n = 2, l will have values 0 and 1. It means that the electron in the second principal energy level may be either in a spherical s-subshell or p-subshell. So, the second energy level has only two subshells, i.e., 2s & 2p. The p-subshells are dumb-bell.
  • For n = 3, l can have values 0, 1, and 2. An electron in the third principal energy level may either be in the s-subshell or p-subshell. So the third energy level has three subshells that are 3s, 3p, & 3d. The d-subshells are leaf-like.

Similarly, the fourth energy level can have four subshells, i.e., 4s, 4p, 4d, & 4f.

The relation between orbital angular momentum and azimuthal quantum number, l is

Orbital angular momentum = [h/ 2𝜋] √[l (l + 1)]

Magnetic Quantum Number (mₗ)

This quantum number refers to the different orientations of the electron cloud in a particular subshell. In other words, the direction of the angular momentum is determined by the magnetic quantum number (mₗ).

The number of orbitals in a specific subshell within a principal energy level is stated by the number of values sanctioned to mₗ, which in turn hangs on the values of l. The possible values of mₗ range +l to -l, including 0 values. The total number of mₗ values gives the total number of orbitals within a given subshell.

Magnetic quantum number rules:

  • For l = 0, i.e., s-subshell, mₗ = 0. Therefore, the s-subshell consists solely of one orbital.
  • For l = 1, i.e., p-subshell, mₗ can be -1, 0, and +1. Therefore, the p-subshell consists of three orbitals.
  • For l = 2, i.e., d-subshell, mₗ can be -2, -1, 0, +1, and +2. Therefore, the d-subshell consists of five orbitals.
  • For l = 3, i.e., f-subshell, mₗ can be -3, -2, -1, 0, +1, +2, and +3. Therefore, the f-subshell consists of seven orbitals.

Spin Quantum Number (mₛ)

This quantum number is denoted by mₛ. It does not arise from the mechanical wave treatment but the spectral proof that an electron, in addition to its revolving motion about the nucleus, also spins about its axis.

(Video) Quantum Numbers | What are the 4 Quantum Numbers? Chemistry

The spin quantum number tells the direction of spin of the electron. The spin can either be anticlockwise or clockwise. The spin quantum number can have only two values which are +1/2 and -1/2. If the positive value indicates clockwise spin, i.e. ↑, upward arrow, and is known as 𝛼-spin. The negative value indicates anti-clockwise spin, i.e. ↓, downward arrow, known as 𝛽-spin.

Quantum Numbers Chart

The relationship between all quantum numbers is represented with the help of a quantum numbers chart.


lmₗmₛNumber of OrbitalsOrbital NameNumber of Electrons

Total Electrons

(K shell)

00+½, -½1




(L shell)

00+½, -½12s2



-1, 0, +1+½, -½32p


(M shell)

00+½, -½13s2


1-1, 0, +1+½, -½33p


2-2, -1, 0, +1, +2+½, -½53d


Information Provided by Four Quantum Numbers

The four quantum numbers give the following information :

  1. n defines the shell number and determines the size of the orbital and the orbital’s energy to a large extent.
  2. There are many subshells in the nth shell. In which subshell the electron lies and decides the shape of the orbital is pointed out by l. There are (2l+1) types of orbitals in a subshell, i.e., the value of l for a one s orbital is 0, for three p orbitals is 1, and for five d orbitals is 2 per subshell. To some limit, l also decides the energy of the orbital in a numerous electrons atom.
  3. mₗ appoints the orientation of the orbital. For a given value of l, mₗ has (2l+1) values, the same as the orbitals’ number per subshell. It suggested that the orbitals’ number equals a lot of ways in which they are positioned.
  4. mₛ refers to the orientation of the spin of the electron.


From the above discussion, it is concluded that four types of quantum numbers allocate the position of an electron in an atom. When the Schrodinger wave equation is calculated for the wave function, 𝛹, the values of three quantum numbers, i.e., n, l, and m, become easy to calculate. Spin quantum number (s) arise due to the electron’s spinning about its axis.

With the help of a quantum numbers chart, you can understand the values of all quantum numbers and memorize them most simply.

Frequently Asked Questions

1. Why is it impracticable to get a principal quantum number as zero or a negative value?

The principal quantum number describes an electron’s electron shell or energy level. It is not feasible for an electron to possess the value of the principal quantum number, n, as zero or a negative value. It is because an atom can’t have a negative value or no value for a principal shell.

2. What are the assigned values of all the four quantum numbers?

The assigned values of all four quantum numbers are:

  • A principal quantum number, i.e., ‘n’, can take all the natural number values.
  • Magnetic quantum number, i.e., ‘mₗ’, can take values from -l to +l, depending upon ‘l’ and hence, ‘n’ too.
  • Azimuthal quantum numbers, i.e., ‘l’, can take values from 0 to (n – 1).
  • The spin quantum number for an electron is either -1/2 or 1/2.

3. Which quantum number decides the magnetic property of an atom?

Due to spin, the electron behaves as a tiny magnet. The electron’s spin is responsible for the magnetic properties of atoms, and molecules of a substance are paired. It behaves as diamagnetic. It is because the magnetic field weakly repels them.

Whereas if atoms or molecules of a substance have one or more unpaired or odd electrons, it behaves as a paramagnetic substance. It is because the magnetic field weakly attracts them.

(Video) what is quantum number and types of quantum number


What is quantum number and its types? ›

What are Quantum Numbers? The set of numbers used to describe the position and energy of the electron in an atom are called quantum numbers. There are four quantum numbers, namely, principal, azimuthal, magnetic and spin quantum numbers.

How many types of quantum numbers are there? ›

In atoms, there are a total of four quantum numbers: the principal quantum number (n), the orbital angular momentum quantum number (l), the magnetic quantum number (ml), and the electron spin quantum number (ms).

What are the 4 quantum number explain each? ›

This tells us that there are two electrons per orbital, or per ml value, one with an ms value of +12 and one with an ms value of −12 . Therefore, n describes the shell, both n and l describe a subshell, n , l , and ml describe an orbital, and all four quantum numbers ( n , l , ml , ms ) describe an electron.

What is quantum number short note? ›

A quantum number is a value used to describe the different energy levels that atoms and molecules have. The state of an electron in an atom or ion is described by four quantum numbers, which produce solutions to the Schrödinger wave equation for the hydrogen atom.

What is quantum number example? ›

NameSymbolValue examples
Principal quantum numbernn = 1, 2, 3, …
Azimuthal quantum number (angular momentum)for n = 3: ℓ = 0, 1, 2 (s, p, d)
Magnetic quantum number (projection of angular momentum)mfor ℓ = 2: m = −2, −1, 0, 1, 2
Spin quantum numbermsfor an electron s = 1/2, so ms = − 1/2, + 1/2

What is the first quantum number? ›

The first quantum number is called the principal quantum number(n). The principal quantum number largely determines the energy of an electron. Electrons in the same atom that have the same principal quantum number are said to occupy an electron shell of the atom.

How many quantum numbers are enough? ›

The four quantum numbers present are the Principal quantum number, Azimuthal quantum number, the Magnetic quantum number, and the Spin quantum number. The quantum number represented by n is the principal quantum number, which indirectly specifies the size of the electron orbital.

Who discovered quantum numbers? ›

Pauli Exclusion Principle: In 1926, Wolfgang Pauli discovered that a set of quantum numbers is specific to a certain electron. That is, no two electrons can have the same values for n, l, ml, and ms.

What is the 4th quantum number called? ›

To distinguish between the two electrons in an orbital, we need a fourth quantum number. This is called the spin quantum number (s) because electrons behave as if they were spinning in either a clockwise or counterclockwise fashion.

What is the 4 Subshell? ›

There are 4 subshells, s, p, d, and f. Each subshell can hold a different number of electrons. The n number determines how many of the subshells make up the shell.

How many sets of 4 quantum numbers are possible? ›

For a multi-electron system, each electron in the system has a unique set of four quantum numbers. Therefore, the system He2− has 4 electrons and has thus four unique sets of four quantum numbers.

Why is it called quantum? ›

It's right there in the name-- the word "quantum" comes from the Latin for "how much" and reflects the fact that quantum models always involve something coming in discrete amounts. The energy contained in a quantum field comes in integer multiples of some fundamental energy.

What is the principal quantum number? ›

In quantum mechanics, the principal quantum number (symbolized n) is one of four quantum numbers assigned to each electron in an atom to describe that electron's state. Its values are natural numbers (from 1) making it a discrete variable.

How is quantum number measured? ›

Look at the Periodic Table of Elements and find the element that you want to know the quantum number for. Find the principal number, which denotes the element's energy, by looking in which period the element is found. For example, sodium is in the third period of the table, so its principal quantum number is 3.

Where is the quantum number located? ›

The number before the orbital name (such as 2s, 3p, and so forth) stands for the principal quantum number, n. The letter in the orbital name defines the subshell with a specific angular momentum quantum number l = 0 for s orbitals, 1 for p orbitals, 2 for d orbitals.

How do you find quantum numbers? ›

The value of n ranges from 1 to the shell of the outermost electron of that atom. The principal quantum number can be determined by looking at the period (numbered row) of the element on the periodic table. The principal quantum numbers of electrons in the S-block and P-block are the same as the period number.

What is principal energy level? ›

In chemistry, the principal energy level of an electron refers to the shell or orbital in which the electron is located relative to the atom's nucleus. This level is denoted by the principal quantum number n. The first element in a period of the periodic table introduces a new principal energy level.

What is the n 1 value? ›

In your case, you have n=1 , which means that the angular momentum quantum number can take 1 possible value. This tells you that the first energy shell can hold a single energy subshell, the s subshell.

What is the quantum number of earth? ›

Hence, the quanta number that characterizes the Earth' revolution is 2.6 × 1074.

What are the p orbitals? ›

p orbital: An atomic orbital having two orbital lobes, and an orbital node at the nucleus. Labeled according to the parallel Cartesian coordinates axis: the px atomic orbital lies along the x-axis, py lies along the y-axis, and pz lies along the z-axis.

Is a good quantum number? ›

Good quantum numbers are often used to label initial and final states in experiments. For example, in particle colliders: 1. Particles are initially prepared in approximate momentum eigenstates; the particle momentum being a good quantum number for non-interacting particles.

Which quantum number has only 2 values? ›

The quantum number ms is known as the spin quantum number which has only 2 allowed values for any atom. The two allowed values are +1/2 and -1/2. It specifically tells the orientation of the spin of the electrons for the atom. The other quantum numbers may have two or more possible values for an atom.

Who is the father of quantum number? ›

Niels Bohr and Max Planck, two of the founding fathers of Quantum Theory, each received a Nobel Prize in Physics for their work on quanta. Einstein is considered the third founder of Quantum Theory because he described light as quanta in his theory of the Photoelectric Effect, for which he won the 1921 Nobel Prize.

Who gave the name quantum? ›

Helmholtz used quantum with reference to heat in his article on Mayer's work, and the word quantum can be found in the formulation of the first law of thermodynamics by Mayer in his letter dated July 24, 1841. In 1901, Max Planck used quanta to mean "quanta of matter and electricity", gas, and heat.

Who named quantum dot? ›

Who invented quantum dots? Quantum dots were discovered in solids (glass crystals) in 1980 by Russian physicist Alexei Ekimov while working at the Vavilov State Optical Institute.

What is shape of p orbital? ›

It has a dumb-bell shape.

What is a subshell? ›

sub·​shell. ˈsəb+ˌ : any of the one or more orbitals making up an electron shell of an atom.

What is 4 Valency called? ›

Carbon has a valency of four, so it is capable of bonding with four other atoms of carbon or atoms of some other monovalent element. This is known as tetravalency of carbon.

What are the 4 orbitals called? ›

There are four basic types of orbitals: s, p, d, and f. An s orbital has a spherical shape and can hold two electrons. There are three p orbitals, each of which has the same basic dumbbell shape but differ in its orientation in space. The p orbitals can hold up to six electrons.

Which Shell has highest energy? ›

Therefore, N shell has maximum energy associated with it as it is the farthest.

How many orbits can n 4 have? ›

Therefore in n=4, number of subshells=4, orbitals=16 and number of electrons =32.

How many electrons can n 3 have? ›

The p subshell has maximum of 3 orbitals Hence total of 6 electrons can fit for n=3 and l=1. Q.

What is quantum used for? ›

Important applications of quantum theory include quantum chemistry, quantum optics, quantum computing, superconducting magnets, light-emitting diodes, the optical amplifier and the laser, the transistor and semiconductors such as the microprocessor, medical and research imaging such as magnetic resonance imaging and ...

What is quantum theory? ›

Quantum theory is the theoretical basis of modern physics that explains the nature and behavior of matter and energy on the atomic and subatomic level. The nature and behavior of matter and energy at that level is sometimes referred to as quantum physics and quantum mechanics.

Why do we use quantum? ›

Quantum computers have the potential to revolutionize computation by making certain types of classically intractable problems solvable. While no quantum computer is yet sophisticated enough to carry out calculations that a classical computer can't, great progress is under way.

What are the properties of quantum numbers? ›

Quantum Numbers:

These can be distinguished by their size, shape, and orientation. To describe each electron in an atom in different orbitals, there are four quantum numbers-principle, azimuthal, magnetic, and spin quantum numbers, which are used.

What is orbital number? ›

The number l, called the orbital quantum number, must be less than the principal quantum number n, which corresponds to a “shell” of electrons. Thus, l divides each shell into n subshells consisting of all electrons of the same principal and orbital quantum numbers.

What is a quantum level in chemistry? ›

Updated on December 11, 2019. A quantum number is a value that is used when describing the energy levels available to atoms and molecules. An electron in an atom or ion has four quantum numbers to describe its state and yield solutions to the Schrödinger wave equation for the hydrogen atom.

What are the 4 quantum numbers of 4s? ›

Therefore the quantum no's of the differentiating electron in 4s-orbital are; n = 4, l = 0, m = 0 and s = +1/2.

What are the 4 quantum numbers for carbon? ›

So the quantum numbers of carbon are 2, 1, 0, +1/2.

What are the three sets of quantum numbers? ›

The three quantum numbers (n, l, and m) that describe an orbital are integers: 0, 1, 2, 3, and so on. The principal quantum number (n) cannot be zero. The allowed values of n are therefore 1, 2, 3, 4, and so on. The angular quantum number (l) can be any integer between 0 and n - 1.

What are the 4 quantum numbers for 3s? ›

So, the possible values of four quantum numbers (principal, angular momentum, magnetic, and spin) of an electron in the 3s orbital are (3,0,0,+1/2)and(3,0,0,−1/2) ( 3 , 0 , 0 , + 1 / 2 ) a n d ( 3 , 0 , 0 , − 1 / 2 ) .

What is the 4 subshell? ›

There are 4 subshells, s, p, d, and f. Each subshell can hold a different number of electrons. The n number determines how many of the subshells make up the shell.

How do you find quantum number? ›

The value of n ranges from 1 to the shell of the outermost electron of that atom. The principal quantum number can be determined by looking at the period (numbered row) of the element on the periodic table. The principal quantum numbers of electrons in the S-block and P-block are the same as the period number.

What does principal quantum number? ›

The numerals, called principal quantum numbers, indicate energy levels as well as relative distance from the nucleus. A 1s electron occupies the energy level nearest the nucleus. A 2s electron, less strongly bound, spends most of its time farther away from the nucleus.

What are the three quantum properties? ›

An electron in an atom has three intrinsic properties: charge, spin and orbital angular momentum; the latter characterizes how the electron orbits around the nucleus.

Is 4s orbital possible? ›

For any atom there is just one 4s orbital.

How many orbitals are in 2p? ›

For any atom, there are three 2p orbitals. These orbitals have the same shape but are aligned differently in space.

How many electrons does n 4 have? ›

Therefore in n=4, number of subshells=4, orbitals=16 and number of electrons =32.


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