Quantum Numbers
Quantum numbers are numbers assigned to all the electrons in an
atom and they describe certain characteristics of the electron. It is
very important to understand Quantum Numbers in order to
understand the Structure of Atom. In this chapter, we’ll learn
everything about Quantum Numbers.
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Introduction to Quantum Numbers
Quantum Number
An atom consists of a large number of orbitals which are
distinguished from each other on the basis of their shape, size and
orientation in space. The orbital characteristics are used to define
the state of an electron completely and are expressed in terms of
three numbers as stated, Principal quantum number, Azimuthal
quantum number and Magnetic quantum number and Spin
Quantum number.
Quantum number are those numbers that designate and distinguish
various atomic orbitals and electrons present in an atom. A set of
four numbers through which we can get the complete information
about all the electrons in an atom, be it energy, location, space, type
of orbital occupied, and even the orientation of that orbital is called
Quantum Numbers.
Browse more Topics under Structure Of Atom

Introduction: Structure of Atom

Atomic Number

Bohr’s Model of Atom

Charged Particles in Matter

Isobars

Isotopes

Mass Number

Neutrons

Rutherford’s Model of an Atom

Thomson’s Model of an Atom

Valency

How are Electrons Distributed in Different Orbits (Shells)?

Sub-Atomic Particles

Atomic Models

Shapes of Atomic Orbitals

Energies of Orbitals

Development Leading to Bohr’s Model of Atom

Emission and Absorption Spectra

Towards Quantum Mechanical Model of Atom
Principal Quantum Number
The Principal Quantum Number represents the principal energy
level or shell in which an electron revolves around the nucleus. It is
denoted by the letter n and can have any integral value except the 0
i.e. n = 1, 2, 3, 4 … ….etc. The energies of the various principal shells
will follow the sequence as :
K < L < M < N < O…..
1 < 2 < 3 < 4 < 5…….
Azimuthal Quantum Number
Azimuthal quantum number, also known as orbital quantum
number determines the subshell to which an electron belongs. As a
matter of result, the number of electronic jump increases and the
number of lines at the same time.

For a given value of n, it can have any integral value ranging from
0 to n – 1.

For the 1st Shell, say K, n =1, you can have only one value i.e. l =
0

For the 2nd Shell, say L, n = 2, you can have two values i.e. l = 0
and 1

For the 3rd Shell, say M, n = 3, you can have three values i.e. l = 0,
1 and 2

For the 4th shells, say N, n = 4, you can have 4 values i.e. l = 0, 1,
2 and 3
Magnetic Quantum Number
Magnetic Quantum Number denoted by the symbol m is what
represents the orientation of atomic orbital in space. The value of
the Magnetic Quantum Number, m, depends on the value of l.
Magnetic Quantum Number can have a total number of (2l + 1).
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
Spin Quantum Number
Spin Quantum Number represents the direction of the spin of the
electrons. This can either be in the direction of clockwise or even
anti-clockwise. Spin Quantum Number is denoted by the symbol s.
It can have about only two values i.e. +1/2 or -1/2
Solved Examples for You
Question: An electron is in one of the 3d orbitals. Give the possible
values of n, l and ml for this electron.
Solution: For the 3d orbital,

Principal quantum number (n) = 3

Azimuthal quantum number (l) = 2

Magnetic quantum number (ml) = – 2 , – 1 , 0 , 1, 2
Question: Calculate the minimum and maximum number of
electrons which have magnetic quantum number m= 1 and spin
quantum number s= 1/2 in chromium
Solution: Spin can either be +1/2 or -1/2. So it is 2 electrons. If one
has spin +1/2, other will have spin -1/2. So it is 2 electrons.
Question: Give the physical significance of Principal Quantum
Number.
Solution: The principal quantum number (n) signifies the size of
the electron cloud.