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Quantum Numbers
Mr Bohr wants to know
Quantum Mechanical Model
Is based on a mathematical probability of where
electrons are located
considers both particle and wave nature of
electrons
wave equation written for each electron
Places electrons in orbitals, not orbits
Quantum Numbers
A set of 4 quantum numbers (and letters)
that describe the probability of an
electron being in a given location in an
atom based on its energy level
Each electron in the atom has a set of 4
unique numbers
Orbitals
region of space within which one can
expect to find an electron
no solid boundaries - “cloud”
Each orbital has an electron capacity of 2
The Hierarchy of Quantum Numbers
space surrounding nucleus divided up into large
volumes called energy levels (1,2,3,4,5,6,7)
Energy levels (shells) subdivided into smaller
volumes called subshells (s,p,d,f)
Subshells contain orbitals
Electrons within orbitals have spin
as shells get further from nucleus, energy, size,
and electron capacity increase
shells, subshells, orbitals, and spin are described
by quantum numbers
Principal Quantum Number - n
 Describes the energy level.
Tells how far away from the nucleus
the electron is
 Energy levels 1 to 7.
 The maximum number of electrons in
n is 2n2.
Orbital Quantum Number - l
 Describes the shape of the region
(sublevel) the electron is probably in.
Tells what sublevel the electron is in
(s,p,d,f)
 Each energy level has n sublevels.
Orbital Quantum Number: - l
Sublevels of different energy levels
may have overlapping energies.
This is shown on the Periodic Table.
Magnetic or Azimuthal Quantum
Number - ml
Tells what axis (x,y,z) the electron is
probably on (the direction in space)
Describes the orbital within a sublevel.
 s has 1 orbital
p has 3 orbitals
d has 5 orbitals
f has 7 orbitals
Orbitals may contain 1 or 2 electrons
Spin Quantum Number - s
 Describes the spin of the electron.
 Electrons in the same orbital must have
opposite spins.
 Possible spins are clockwise, +1/2, and
counterclockwise, -1/2.
s Orbital
p Orbitals
y
y
z
x
y
px
x
z
py
x
pz
z
d Orbitals
y
y
z
z
y
z x
x
dx2–
2
y
dxy
x
y
z
x
dz2
y
z
x
dxz
dyz
Pauli Exclusion Principle
No two objects can be in the same
place at the same time
OR:
No two electrons in an atom have the
same set of four quantum numbers.
Electron Configuration
1s2 2s2 2p6 3s2 3p5
The large # is the electron energy level.
The small letter is the sublevel.
The superscript is the number of electrons in the
sublevel.
Read this from the Periodic Table.
Electron Configuration
1s2 2s2 2p6 3s2 3p6 4s2 3d3
1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2
4d9
Write the e-conf. for Bromine.
Write the e-conf. for Lanthanum.
Hund‘s Rule
Electrons will enter empty orbitals of
equal energy when they are available.
Electrons Indicated by Shell and
Subshell
Symbolism
#electrons
nl#
number
letter
Electrons Indicated by Shell and
Subshell
Symbolism
#electrons
nl#
number
3s2
letter
5p5
4f14
Mr. Schroedinger has lost his cat !
End
Quantum
Numbers
24
22
20
18
16
14
12 H
10
8
V 6
o 4
l 2
t
1 2
s
E
l
e
c
t
r
o
n
He
1 st Ionization Energy
Ne
F
Ar
N
C
Be
P
O
Mg
Cl
S
B
Si
Al
Li
Na
3
4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
Atomic Number