Quantum numbers are essential for describing the position and energy of electrons in an atom, consisting of four types: principal, subsidiary, magnetic, and spin quantum numbers. They define energy levels, shapes, orientations of orbitals, and the behavior of electrons as described by principles such as the Pauli exclusion principle, Hund's rule, and the Aufbau principle. Each quantum number plays a critical role in understanding electron configurations and the structure of atoms.

1. QUANTUM NUMBERS

2. WHAT IS A QUANTUM NUMBER?
The set of numbers used to describe the
position and energy of the electron in an atom
are called quantum numbers.

3. Orbitals
● This is the region or space where there is
high probability of locating an electron.

4. Four Quantum Numbers
● Principal quantum number
● Subsidiary or Azimuthal quantum number
● Magnetic quantum number
● Spin quantum number

5. THE PRINCIPAL QUANTUM
NUMBER (n)
ENERGY LEVELS OR
SHELLS
Energy levels in an
atom are sometimes
called shells. The
principal quantum
number (n) describes
the size and energy of
an atomic orbital. (n =

6. THE SUBSIDIARY OR AZIMUTHAL
QUANTUM NUMBER (l) :
ENERGY SUBSHELLS i.e s,
p, d and f

7. THE SUBSIDIARY OR AZIMUTHAL
QUANTUM NUMBER (l)
whole number values range from 0 to n-1 for
each value of n
Examples : when n = 1, l = 0
when n = 3, l = 0, 1, and 2

8. SUBSIDIARY QUANTUM NUMBERS
AND THEIR ENERGY LEVELS
How many orbitals exist at n=1?
How many orbitals exist at n=3? What are they?

9. MAGNETIC QUANTUM NUMBER (m)
This shows the NUMBER OF ORBITALS in
each energy sublevel.
- represented by whole number values between
+l and -l including 0
- the number of different values that ml can
have is equal to the number of orbitals that
are possible
E.g when n= 1, l = 0, m= 0. This means there
is ONE orbital in subenergy level s.

11. MAGNETIC QUANTUM NUMBER (ml)
EXAMPLE:
When l = 1, how many
different orbitals are
there?

13. SHAPES AND ORIENTATION OF
ORBITALS
Each orbital has a
unique probability
distribution, shape,
and orientation.
Let’s start with “s”
orbitals. Think of
s = spherical!

14. p ORBITALS
- have two lobes
separated by a node
at the nucleus (think
dumbbell shaped)
- can exist in any of 3
dimensions and are
labeled using
xyz coordinate
system

15. VIDEO : s and p orbitals

16. d ORBITALS
- the first d orbitals occur in n=3 energy level
- there are 5 of them…

17. SPIN QUANTUM NUMBER (ms)
This is the quantum
number that relates to
the spin of the
electron. It can either
be +½ or -½.

18. THE PAULI EXCLUSION PRINCIPLE
This principle states that two electrons in the
same orbital of an atom cannot have same
values for all four quantum numbers
“In a given atom, no two electrons can have the
same set of four quantum numbers (n, l, m, and s)”
Since electrons in the same orbital have the
same values for n, l, and ml, they must have
different ms values.

19. Hund’s Rule
This states that electrons occupy each orbital
singly before pairing takes place in a
degenerate orbital.

20. Aufbau Principle
This principle states that electrons are fed into
orbitals starting at the lowest energy level
before filling higher energy level.

21. EXAMPLE 1:
For the principal quantum number n=5,
determine the value(s) of the secondary
quantum number l and the types of orbitals in
each case.

22. EXAMPLE 2:
How many possible values of ml are there for
l = 0, 1, 2, and 3? What pattern do you notice in
these numbers?

23. Trying to learn about
Quantum Theory from
Einstein himself!
Good luck
O.A. TIJANI