The Electromagnetic Spectrum
Quantum Mechanics
A way to describe electron behavior
V
I
B
G
Y
O
R
…describes the wave nature of light
Wave Comparison
All electromagnetic waves
can be described by the equation:
Red Light
c=f
• Low frequency
c = speed of light = 3.0 x 108 m/s
 (wavelength) is inversely proportional to f (frequency)
nm = 1 x 10-9 m
• Long wavelength
Violet Light
• High frequency
•Short wavelength
As wavelength increases,
frequency decreases
emission
Electron Energy as a Wave
• All of our understanding of electrons comes
from radiant energy (‘light’) they emit.
• Electrons themselves and the light they emit
can be thought of (modeled) as:
particles (photons)
or as
waves (electromagnetic radiation)
1
Max Planck
studied the wavelengths of emitted by electrons…
and related their frequency to the energy difference between
shells.
E = hf
(Energy difference) = (Planck’s constant) x (frequency)
E
Spectral Lines
When electrons “jump” from a higher
shell to a lower shell, they emit light.
All of the “jumps” that occur in an
atom of on element result in a signature
EMISSION SPECTRUM.
…for that element. Below is Mercury’s spectrum:
Make the electrons gain energy…
• Let’s look at a hydrogen atom
by adding electricity or heat; electrons make a
quantum leap to a higher energy level (shell)
The electrons lose (release) energy
…and they fall back to their ground state;
the lost energy takes the form of light,
which we study.
Changing the energy
• May fall down in steps
• Each with a different energy
2
Spectral Lines
{
{
{
When electrons “jump” from a higher
shell to a lower shell, they emit light.
All of the “jumps” that occur in an
atom of on element result in a signature
EMISSION SPECTRUM.
…for that element. Below is Mercury’s spectrum:
to make a long story short…
Niels Bohr
Albert Einstein
Werner Heisenberg
Wolfgang Pauli
Louis de Broglie
Max Planck
Erwin Schrödinger
and others…
De Broglie
Essentially the model went from
…described
electrons’
location and
behavior by
developing:
to
Bohr
Quantum Mechanical Theory
“the new physics”
Nodal Surfaces
A nodal surface is a region that defines the border
of an orbital. This is where the probability function
equals zero. Electrons CAN NOT exist in this area.
Nodal surfaces are
spherical for the “s”
orbitals.
Nodal surfaces are
NOT spherical for
other orbitals.
de Broglie
“Where” are the electrons?
Like Bohr said,
electrons are found in shells…(“energy levels”)
…but all shells contain subshells…
…all subshells contain orbitals…
…and every orbital contains two electrons.
3s orbital
2p orbital
Whoa; that’s four levels of giving an electron’s “address”!
3
Schrodinger
proposed
4 Quantum Numbers
to describe the location of an electron
n
the Principal Quantum Number
(describes the SHELL)
l
the Secondary Quantum Number
(describes the SUBSHELL)
m1
the Magnetic Quantum Number
ms
the Spin Quantum Number
n
the Primary Quantum Number
• the energy level (shell) of the electron.
• the average distance from the nucleus.
• n can be 1 through 7 .
• there can only be 2n2 electrons in a shell.
(describes the ORBITAL)
(describes the SPIN)
“Where” are the electrons?
Like Bohr said,
electrons are found in shells…(“energy levels”)
…but all shells contain subshells…
…all subshells contain orbitals…
…and every orbital contains two electrons.
There are s, p, d and f subshells
Each shell has n subshells.
the n = 1 shell only has one subshell:
(an “s”)
the n = 2 shell has two subshells:
(an “s” and a “p”)
l
the Secondary Quantum Number
• the subshell (“sublevel”) of the electron
• each shell has n subshells.
• Names of subshells:
s
(l = 0)
p
(l = 1)
d
(l = 2)
f
(l = 3)
“Where” are the electrons?
Like Bohr said,
electrons are found in shells…(“energy levels”)
…but all shells contain subshells…
…all subshells contain orbitals…
the n = 3 shell has three subshells:
(an “s” a “p” and a “d”)
…and every orbital contains two electrons.
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Orbitals Orbitals
An orbital is a 3-dimensional region of space where the electron
is likely to be found.
An orbital is not an
orbit! It is a
“probability map”
(“probability
density
distribution”)
m1 the Magnetic Quantum Number
• tells you which orbital the electron is in.
• each orbital has a specific shape & orientation.
• Shapes correspond to probability of finding an
electron in that area.
• each orbital can hold 2 electrons.
each subshell has a different number of orbitals!
There is only one orbital
in an s subshell.
AnAn
orbital
is not
orbit! It is a “probability
map”
orbital
is a an
3-dimensional
region of space
“probability
density
distribution”
where
the electron
is likely
to be found.
orbitals of the p subshell:
orbitals of the d subshell:
• only start at the
third shell (n=3)
• there are 5
orbitals in the d
subshell.
• only start at the second shell (n=2)
• there are 3 orbitals in the p subshell.
• they have different orientations
px orbital
m1 = -1
py orbital
m1 = 0
orbitals of the f subshell:
• only start at
the fourth
shell (n=4)
• there are 7
orbitals in the
f subshell.
s orbitals are spherical.
pz orbital
m1 = +1
“Where” are the electrons?
Like Bohr said,
electrons are found in shells…(“energy levels”)
…but all shells contain subshells…
…all subshells contain orbitals…
…and every orbital contains two electrons.
5
ms
the Spin Quantum Number
• the last quantum number describes spin
• Remember; only 2 e- per orbital
• the 2 electrons in an orbital will always
have opposite spins.
ms ( “spin” ) can only be +
½ or – ½
How many electrons in each
subshell?
Well, there are only 2 electrons
allowed per orbital, so:
•
•
•
•
s subshell =
p subshell =
d subshell =
f subshell =
1 orbital 
3 orbitals 
5 orbitals 
7 orbitals 
2 e6 e10 e14 e-
Remember…
Summary
# of
Max
orbitals electrons
Each shell has n subshells;
Starts at
energy level
s
1
2
1
p
3
6
2
d
5
10
3
f
7
14
4
So…
the n = 1 shell only has one subshell:
(an “s”)
the n = 2 shell has two subshells:
(an “s” and a “p”)
the n = 3 shell has three subshells:
(an “s” and a “p” and a “d")
Electron Diagrams
Writing Electron Configurations:
Each arrow represents an electron.
Arrow direction indicates spin.
Fill from the inside out, just like Bohr Model diagrams
Example: Cr
3s
1s
Cr
Cr
2s
3p
3d
4s
2p
1s22s22p63s23p64s23d4
[Ar]
4s23d4
“Hund’s Rule”;
one e- in each
orbital before
pairing
Energy Level
n
4
2p
Subshell
(s, p, d or f)
Number of
electrons in
that subshell
1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2 4d10 5p6
6s2 4f14… etc.
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Some subshells overlap:
So, we fill in this order:
1s2
Electron Diagrams
2s2 2p6 3s2 3p6 4s2 3d10 4p6
valence
electrons
are in ….
Each arrow represents an electron.
Arrow direction indicates spin.
5s2
4d10
Orbitals and the
Periodic Table
Fill from the inside out, just like Bohr Model diagrams
s orbitals
Example: Cr
d orbitals
3s
1s
2s
3p
p orbitals
3d
4s
2p
Cr
1s22s22p63s23p64s23d4
Cr
[Ar] 4s23d4
“Hund’s Rule”;
one e- in each
orbital before
pairing
f orbitals
The secret of periodicity:
Electron Configuration
• Let’s determine the electron configuration
for Phosphorus (P)
• Need to account for 15 electrons
7
7p
6p
6d
5p
4d
5d
4p
4f
3d
4s
3s
5f
3p • The first to electrons go
2p
2s
into the 1s orbital
• Notice the opposite spins
• only 13 more
1s
• 1s2
• 2 electrons
Let’s Try It!
• Write the electron configuration for
the following elements:
He
1s2
Li
1s2 2s1
N
1s22s22p3
Ne
1s22s22p6
K
Zn
7s
6s
5s
1s2 2s2 2p6 3s2 3p6 4s2 3d10
7p
6p
6d
5p
4d
5d
5f
4f
4p
3d
•
The
last
three electrons
3p
go into the 3p orbitals.
2p • They each go into
seperate shapes
• 3 upaired electrons
• 1s22s22p63s23p3
4s
3s
2s
1s
Aufbau Principle: (“Building Up”)
7s 7p 7d 7f
6s 6p 6d 6f
5s 5p 5d 5f
4s 4p 4d 4f
3s 3p 3d
2s 2p
1s
Increasing energy
Increasing energy
7s
6s
5s
Fill from the bottom up following
the arrows
7s 7p 7d 7f
6s 6p 6d 6f
5s 5p 5d 5f
4s 4p 4d 4f
3s 3p 3d
2s 2p
1s
• 1s2 2s2 2p6 3s2
3p6 4s2 3d10 4p6
5s2 4d10 5p6 6s2
4f14 5d10 6p6 7s2
5f14 6d10 7p6
• 108 electrons
Abbreviated
Notation
• A way of abbreviating long
electron configurations
• Since we are only concerned
about the outermost electrons,
we can skip to places we know
are completely full (noble
gases), and then finish the
configuration
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Abbreviated
Notation
• Chlorine
Longhand is
1s2 2s2 2p6 3s2 3p5
You can abbreviate the first
10 electrons with [Ne]
(replaces 1s2 2s2 2p6 )
The next energy level after
Neon is 3
So you start at level 3 and
finish by adding 7 more
electrons to bring the
total to 17
[Ne] 3s2 3p5
Abbreviated
Notation
• Step 1: Find the closest noble gas to
the atom (or ion), WITHOUT GOING
OVER the number of electrons in the
atom (or ion). Write the noble gas in
brackets [ ].
• Step 2: Find where to resume by finding
the next energy level.
•
Step 3: Resume the configuration
until it’s finished.
Practice Shorthand Notation
• Write the shorthand notation for each of the
following atoms:
Cl
K
Ca
I
Bi
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