This document describes atomic orbitals and the properties of electrons within them, focusing on four quantum numbers: principal, azimuthal, magnetic, and spin. These numbers define an electron's energy, shape, orientation, and spin state, crucial for understanding electron behavior in an atom. Examples illustrate how to determine these quantum numbers from elements in the periodic table.

1. Lesson 4
Prepared by: Cristy Joy L. Aranas

2. These describe the atomic
orbitals as well as the
properties of the electrons in
those orbitals.

3. these numbers are used to describe completely the
movement and trajectories of each electron within an atom
Principal
Quantum
Number
Azimuthal
Quantum
Number
Magnetic
Quantum
Number
Spin
Quantum
Number

4. • describes the energy of an
electron and the most
probable distance of the
electron from the nucleus.
• represented with the
symbol n
• the larger the number n is,
the farther the electron is
from the nucleus

5. • there exists no atoms with
zero or a negative amount
of energy levels/principal
shells.
How to Find the Principal Quantum
Number?
can be determined from the PERIOD
in which the element resides in the
periodic table.

6. Cl :
Rb :
O :
Fe :
n = 3
n = 5
n = 2
n = 4

7. • also known as angular
momentum quantum
number, describes the
shape of the subshell in
which the electron is
present
• represented with the
symbol l

8. There are 4 sub-shells/
orbitals: s, p, d, f

9. How to Find the Azimuthal Quantum
Number?
identify the orbitals in which the
electrons reside
Azimuthal
Quantum
Number (l )
orbital
designation
0 s-orbitals
1 p-orbitals
2 d-orbitals
3 f-orbitals

11. Cl :
Rb :
O :
Fe :
l = 1
l = 0
l = 1
l = 2

12. • It splits the sub-shells (such
as s,p,d,f) into individual
orbitals and places the
electron in one of them.
• represented with the
symbol 𝒎𝒍
• It defines the orientation in
space of a given orbital of
particular energy (n) and
shape (I).

13. • It splits the sub-shells (such
as s,p,d,f) into individual
orbitals and places the
electron in one of them.
• represented with the
symbol 𝒎𝒍
• It defines the orientation in
space of a given orbital of
particular energy (n) and
shape (I).

15. Cl :
Rb :
O :
La :
Fe :
l = 0
l = 1
l = 2
l = 2
l = 1 𝒎𝒍 = 0
𝒎𝒍 = 0
𝒎𝒍 = -1
𝒎𝒍 = -2
𝒎𝒍 = -2

16. • represents the electron’s
spin and may have only
two possible values, +1/2
and -1/2
• represented with the
symbol 𝒎𝒔
• When 𝒎𝒔 = +1/2, the electron
is in “spin-up” state
• When 𝒎𝒔 = -1/2, the electron
is in “spin-down” state

17. O :
La :
Fe :