Quantum Model and
Quantum Numbers
Quantum Model of the Atom
• Quantum Mechanics – the branch of physics that
uses mathematical equations to describe the wave
properties of subatomic particles.
• Orbital – a wave function that predicts an
electron’s energy and location within an atom.
Quantum Numbers
• Four numbers used to describe a specific
electron in an atom.
• Each electron has its own specific set of quantum
numbers.
The first quantum number
• Principal quantum number, Symbol “n”
• Indicates the energy level and distance from the
nucleus of an electron (same as period number)
• Higher n  farther from nucleus and greater energy
• n = 1, 2, 3… (always a positive whole number)
• The greatest number of electrons possible in each
energy level is 2n2.
The second quantum number
• Orbital shape quantum number
• Symbol “l ”
• Atoms with many electrons showed spectrum with
many lines, some close together and others further
a part.
• Scientists hypothesized that there were sublevels
within the main energy levels.
• Each of these sublevels (orbitals) has a different shape or
region with most likelihood of finding an electron.
• Positive integer ranging from 0-3
• Maximum Value of “n-1”
•
•
•
•
l=0
l=1
l=2
l=3
is designated a s orbital
is designated a p orbital
is designated a d orbital
is designated a f orbital
• Total number of sublevels possible for each energy
level is n2
Orbital Shapes
Want to see the orbitals?
• http://winter.group.shef.ac.uk/orbitron/
The third quantum number
• Magnetic Quantum Number (m l )
• Describes an orbital’s orientation
• Each sublevel orbital s, p, d, f has its own shape, but
can have a different orientation about the nucleus.
• For example: A p orbital can have 3 different
orientations
• Allowed values m l = –l  +l
The First three Quantum Numbers
Questions
1. If n = 3, what are the allowed values for l and ml
and what is the total number of orbitals in this
energy level?
2. a) What are the possible values for ml
if n = 5 and l =1?
b) What kind of orbital is described by these
quantum numbers?
c) How many orbitals can be described by these
quantum numbers?
The Fourth Quantum Number
• Spin quantum number (ms)
• Specifies the direction in which an electron is
spinning (either up or down).
• Pauli Exclusion Principle – (Wolfgang Pauli 1925) only two electrons of opposite spin can occupy one
orbital.
• Therefore each electron is given a value of
+½ or –½
• By convention, the first electron
is given the positive value +½
Summary Chart of the Four Quantum
Numbers
Name
Symbol
Principal
n
Orbital
Shape
l
Magnetic
ml
Spin
ms
Allowed
Values
positive
integers
1,2,3…
Integers
from
0 to (n-1)
Integers –l
to +l
+½ or –½
Property
Orbital size
and energy
Orbital
shape
Orbital
orientation
Electron
Spin
Direction