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# Quantum Numbers

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Last updated date: 21st Sep 2024
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## What are Quantum Numbers?

The energy and location energy of an electron in an atom is specified by quantum numbers, which are a collection of integers. There are four types of quantum numbers they are principal,  magnetic, azimuthal and spin quantum numbers. The route and mobility of an electron in an atom can be described using quantum numbers. Whenever the quantum numbers of all the electrons are summed together, the  Schrodinger equation must be fulfilled.

### Types of Quantum Numbers

1. Principal Quantum Number

2. Azimuthal Quantum Number

3. Magnetic Quantum Number

4. Spin electron Quantum Number.

### Principal Quantum number

1. It is denoted by n. It refers to the electron shell with the most electrons. It gives the electron's likely distance from the nucleus. The bigger the value of 'n,' the greater the distance between the electron and the nucleus.

2.  It also indicates the size of the electron's orbital and energy level. As a result, a bigger 'n' signifies a larger orbital size and thus a larger atomic radius.

3.  The force of attraction between an electron and a nucleus is weaker when the atomic radius is big. As a result, the ionisation energy, or the energy required to remove electrons, is lower in atoms with tiny radii.

4.  Any positive integer can be used as the value of 'n.' Because an atom can't have either zero or negative energy, it can't be zero or a negative integer when n = 1, the ground state or lowest energy shell is designated as the innermost shell or first primary shell.

5. By absorbing energy or photons, an electron can gain energy and hop to higher shells, increasing the value of 'n'.

6.  If it loses energy, it returns to lower shells, and the value of 'n' drops, allowing photons to be emitted.

### Azimuthal Quantum Number

1. The azimuthal (or the orbital angular momentum) quantum number is defined as the determination of the shape of an orbital. Its value is equal to the total number of angular nodes in the orbital and is indicated by the symbol 'l.'

2. The azimuthal quantum number can suggest an s, p, d, or f subshell, all of which have different forms. This value is determined by (and limited by) the primary quantum number, i.e. the azimuthal quantum number varies between 0 and 1. (n-1).

3. For example, if n = 3, the azimuthal quantum number can be 0, 1, or 2. The resulting subshell is an's' subshell when l=0. When l=1 and l=2, the resulting subshells are 'p' and 'd' subshells, respectively (respectively). When n=3, the three subshells that can be used are 3s, 3p, and 3d.

4. In another example, the possible values of l are 0, 1, 2, 3, and 4 when the value of n is 5. There are three angular nodes in the atom if l = 3.

### Magnetic Quantum Number

1. The magnetic quantum number determines the  subshell's overall number of orbitals and their orientation. The symbol ‘m’is used to represent it.

2. This number shows the orbital angular momentum projected along a given axis. The azimuthal (or orbital angular momentum) quantum number determines the value of the magnetic quantum number.

3.  The value of ‘m’ is dependent on the value of ‘ℓ’. Magnetic quantum numbers can have a total of (2 ℓ + 1) values. The value of ml for a particular value of l is in the range of -l to +l. As a result, it is indirectly affected by the value of n.

### Electron Spin Quantum Number

1. The values of n, l, and ml have no bearing on the electron spin quantum number. The symbol ‘ms’ represents the value of this number, which indicates the direction in which the electron is spinning.

2. The value of ms provides information on the electron's spin direction. The electron spin quantum number has two potential values: 1/2 and -1/2. The positive number of ms denotes an upward spin on the electron, often known as pin up,' and is represented by the symbol ↑. If ms is negative, the electron in question has a downward spin, or spin down,' which is represented by the symbol. The ability of the atom to create a  magnetic field is determined by the magnitude of the electron spin quantum number. The value of ms can be approximated as 1/2.

### Need of Quantum Numbers

To characterise the location of an electron in an associated atom, we utilise a sequence of particular integers known as quantum numbers. The properties of atomic orbitals and the electrons in those orbitals are described by quantum numbers. There are a total of four  quantum numbers that  characterise the configuration of an electron in an atom or ion. Regard them as significant variables in an equation describing the three-dimensional location of electrons in a particular atom.Electrons first occupy the orbitals singly and then they pair up. In each orbital a maximum of two electrons can fit and their orientation will be opposite to each other. If one electron is in a spin up position, the other will be spin down. The following illustration explains this.

• It also suggests whether the atom has the ability to produce magnetic fields or not. Due to spin an electron behaves like a small magnet.

• If in an atom all the electrons are paired in the orbitals, their spins with opposite values cancel each other and the atom is said to be diamagnetic. If we add up their spins the total is zero and they repel magnetic fields.

Electronic configuration of Mg at ground state (all electrons are paired so its diamagnetic)-

• If an atom contains unpaired electrons in the orbitals, the electron in the orbital has a net spin and the spins do not cancel each other out. As a result the atom has a net spin and is attracted to a magnetic field. Such atoms are called paramagnetic. Electronic configuration of O- - It has 1 unpaired electron,  so it's paramagnetic.

Electrons have certain characteristics such as configuration, spin and position in an atom. These characteristics are defined by quantum numbers.

### What are Quantum Numbers?

There are certain values assigned to every electron in an atom. These values are called quantum numbers. They give the exact address of an electron in an atom.

According to Pauli’s Exclusion principle each electron in an atom has a unique set of quantum numbers i.e. no two electrons have the same combination of quantum numbers.

The quantum numbers of all electrons in an atom is a wave function that must comply with the Schrödinger equation.

### Quantum Numbers are Important Because They

1. Help in determining electronic configuration of an atom.

2. Give information about the probable location of electrons.

3. Help in understanding characteristics of an atom such as their ionization energy and atomic radius.

## There are Four Types of Quantum Numbers

 Number Symbol Possible Values Principal Quantum Number n 1,2,3,4,….. Azimuthal Quantum Number ℓ 0,1,2,3,…., (n-1) Magnetic Quantum Number ml - ℓ to +ℓ -1,0,1… Spin Quantum Number ms +1/2, -1/2

 Sublevel ℓ mℓ s 0 0 p 1 -1, 0, +1 d 2 -2, -1, 0, +1, +2 f 3 -3, -2, -1, 0, +1, +2, +3

Example: The possible total number of orbitals in a given subshell for n= 4 and ℓ = 3 is (2*3+ 1) 7. The values of magnetic quantum numbers will be -3, -2, -1, 0, +1, +2, and +3. Each orbital can accommodate 2 electrons so there will be a total of 14 or (7 *2) electrons in 3f subshell.

 Subshells Orbitals Maximum Number of Electrons s 1 2 p 3 6 d 5 10 f 7 14

### Summary

The four quantum numbers can be summarized as follows:

 Name Symbol Allowed Values Property Principal n Positive integers 1,2,3… Orbital size and energy level Azimuthal ℓ Integers from 0 to (n- 1) Orbital shape (subshells) Magnetic ml Integers – ℓ to +l Orbital orientation Spin ms +1/2 or -1/2 Electron spin direction

## FAQs on Quantum Numbers

1. Explain Quantum Energy?

In physics, we can say that the quantum is a discrete natural unit, or bundle, of energy, charge, angular momentum, or any other physical attribute. Photons can be defined as particle-like packets of light that are typically used to describe quanta with other forms of electromagnetic radiation such as X rays and gamma rays.

2. Explain Principal Energy levels?

The shell or orbital in which an electron sits in relation to the nucleus of the atom is referred to as the electron's main energy level. This level is denoted by the primary quantum number n. The first element introduces a new key energy level inside the time of the periodic table.