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Electrons in Atoms
Greek Idea
Democritus and
Leucippus
 Matter is made up
of indivisible
particles
 Dalton - one type
of atom for each
element

Thomson’s Model
Discovered electrons
 Atoms were made of
positive stuff
 Negative electron
floating around
 “Plum-Pudding”
model

Rutherford’s Model
Discovered dense
positive piece at
the center of the
atom
 Nucleus
 Electrons moved
around
 Mostly empty
space

Bohr’s Model
 Why
don’t the electrons fall into the
nucleus?
 Move like planets around the sun.
 In circular orbits at different levels.
 Amounts of energy separate one
level from another.
Bohr’s Model
Nucleus
Electron
Orbit
Energy Levels
Bohr’s Model
Increasing energy
Fifth
Fourth
Third
Second
First
Nucleus
Further away
from the
nucleus means
more energy.
 There is no “in
between”
energy
 Energy Levels

The Quantum Mechanical Model

Energy is quantized. It comes in chunks.
Quanta - the amount of energy needed
to move from one energy level to another.
Since the energy of an atom is never “in
between” there must be a quantum leap
in energy.
The Quantum Mechanical Model

Schrodinger derived an equation that
described the energy and position of the
electrons in an atom
Heisenberg Uncertainty Principle – it is
impossible to know both the position and
energy (momentum) of an electron at the
same time.
Photons – light particles that allow us to
make observations
The Quantum Mechanical Model
Things that are very small behave
differently from things big enough to see.
 Wave-Particle Duality of Nature – an
electron can behave like a wave or a
particle depending on what is being
studied.

The Quantum Mechanical Model

Describes the location of an electron by
using four quantum numbers:

1st - Principle Energy Level (n)
2nd – Sublevel (l)
• 3rd - Angular Momentum (m)
– 4th – Spin (s)

Each level is getting more specific for
the location of the electron.
1st Quantum Number

Principal Energy Level (n) = the energy
level of the electron.
There are 7 main energy levels for all
known elements today.
The value equals the row of the
periodic table (exception is the d and f
sublevels)
2nd Quantum Number


Within each energy level the complex math of
Schrodinger’s equation describes several
shapes.
Sublevel – describes the shape of the orbital.
Orbital – probable region where there is an
electron.
The value is associated with the type of
orbital. S = 0; p = 1; d = 2; f = 3
s orbitals
Spherical
shaped
 Start at first
energy level
 Each s orbital
can hold
2 electrons

p orbitals




Start at the second energy level
3 different directions
dumbbell shaped
Each can hold 2 electrons – 6 total
p Orbitals
d orbitals
Start at the third energy level
 5 different shapes
 Each can hold 2 electrons – 10 total

f orbitals
Start at the fourth energy level
 7 different shapes
 Each can hold 2 electrons – 14 total

f orbitals
Summary
# of
Max
shapes electrons
Starts at
energy level
S
1
2
1
p
3
6
2
d
5
10
3
f
7
14
4
Electron Configurations
Use the 1st and 2nd quantum numbers
to describe an atoms electrons.
 Aufbau principle- electrons enter the
lowest energy first.
 This causes difficulties because of the
overlap of orbitals of different energies.

The easy way to remember
7s 7p 7d 7f
6s 6p 6d 6f
5s 5p 5d 5f
4s 4p 4d 4f
3s 3p 3d
2s 2p
1s
•
2
1s
• 2 electrons
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
•
2
2
1s 2s
• 4 electrons
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
•
2
2
6
2
1s 2s 2p 3s
• 12 electrons
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
•
2
2
6
2
1s 2s 2p 3s
6
2
3p 4s
• 20 electrons
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
•
2
2
6
2
1s 2s 2p 3s
6
2
10
6
3p 4s 3d 4p
5s2
• 38 electrons
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
•
2
2
6
2
1s 2s 2p 3s
6
2
10
6
3p 4s 3d 4p
5s2 4d10 5p6 6s2
• 56 electrons
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
•
2
2
6
2
1s 2s 2p 3s
6
2
10
6
3p 4s 3d 4p
5s2 4d10 5p6 6s2
4f14 5d10 6p6 7s2
• 88 electrons
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
•
2
2
6
2
1s 2s 2p 3s
6
2
10
6
3p 4s 3d 4p
5s2 4d10 5p6 6s2
4f14 5d10 6p6 7s2
5f14 6d10 7p6
• 108 electrons
Orbital Diagram
A visual representation of the
electrons orbital arrangement.
 Write the electron configuration for P.
 1s2 2s2 2p6 3s2 3p3

1s
2s
2p
3s
3p
4s
3d

Hund’s Rule- When electrons occupy
orbitals of equal energy they don’t
pair up until they have to .

1s2
1s
2s
2p
3s
3p
4s
3d

Hund’s Rule- When electrons occupy
orbitals of equal energy they don’t
pair up until they have to .

1s2 2s2 2p6
1s
2s
2p
3s
3p
4s
3d
• 1s22s22p63s23p3
• 3 Unpaired electrons - paramagnetic
1s
2s
2p
3s
3p
4s
3d
3rd Quantum Number



Angular Momentum (m) - describes the
orientation
The value is (– l) to (+l)
Each orbital within the sublevel is assigned
a number
s = 0
p = -1; 0; +1
d = -2; -1; 0; +1; +2
f = -3; -2; -1; 0; +1; +2; +3
3rd Quantum Number

The value is (– l) to (+l)

Each orbital within the sublevel is assigned a number
s = 0 p = -1; 0; +1
d = -2; -1; 0; +1; +2
f = -3; -2; -1; 0; +1; +2; +3
0
0 -1 0 +1 0 -1 0 +1 0
1s
2s
2p
3s
3p
4s
-2 -1 0 +1 +2
3d
4th Quantum Number
Spin (s) – each orbital contains two
electrons with different spins.
 Pauli Exclusion Principle- at most 2
electrons per orbital – must have
different spins
Value is either +½ or -½
Indicated by an up or down arrow

4th Quantum Number

Spin –
Up arrow = +½
Down arrow = -½
0
0 -1 0 +1 0 -1 0 +1 0
1s
2s
2p
3s
3p
4s
-2 -1 0 +1 +2
3d
All Four Quantum Numbers
1st – Energy Level = 3
2nd – Sublevel Value (p) = 1
3rd – Angular Momentum Value = +1
4th – Spin – Up arrow = +½
0
0 -1 0 +1 0 -1 0 +1 0
1s
2s
2p
3s
3p
4s
-2 -1 0 +1 +2
3d
Exceptions to Electron
Configuration
Orbitals fill in order
Lowest energy to higher energy.
 Adding electrons can change the
energy of the orbital.
 Half filled orbitals have a lower
energy.
 Makes them more stable.
 Changes the filling order

Write these electron
configurations
Titanium - 22 electrons
 1s22s22p63s23p64s23d2
 Vanadium - 23 electrons
1s22s22p63s23p64s23d3
 Chromium - 24 electrons
 1s22s22p63s23p64s23d4 is expected
 But this is wrong!!

Chromium is actually
1s22s22p63s23p64s13d5
 Why?
 This gives us two half filled orbitals.
 Slightly lower in energy.
 The same principal applies to copper.

Copper’s electron
configuration
Copper has 29 electrons so we
expect
 1s22s22p63s23p64s23d9
 But the actual configuration is
 1s22s22p63s23p64s13d10
 This gives one filled orbital and one
half filled orbital.
 Remember these exceptions

Light
The study of light led to the
development of the quantum
mechanical model.
 Light is a kind of electromagnetic
radiation.
 Electromagnetic radiation includes
many kinds of waves
 All move at 3.00 x 108 m/s ( c)

Parts of a wave
Crest
Wavelength
Amplitude
Orgin
Trough
Parts of Wave
Orgin - the base line of the energy.
 Crest - high point on a wave
 Trough - Low point on a wave
 Amplitude - distance from origin to crest
 Wavelength - distance from crest to
crest
 Wavelength - is abbreviated l Greek
letter lambda.

Frequency
The number of waves that pass a
given point per second.
 Units are cycles/sec or hertz (hz)
 Abbreviated n the Greek letter nu

c = ln
Frequency and wavelength
Are inversely related
 As one goes up the other goes down.
 Different frequencies of light is
different colors of light.
 There is a wide variety of frequencies
 The whole range is called a spectrum

High
Low
energy
energy
Radio Micro Infrared
Ultra- XGamma
waves waves .
violet Rays Rays
Low
High
Frequency
Frequency
Long
Short
Wavelength
Wavelength
Visible Light
Atomic Spectrum
How color tells us about atoms
Prism
White light is
made up of all the
colors of the
visible spectrum.
 Passing it through
a prism separates
it.

If the light is not white
By heating a gas
with electricity we
can get it to give
off colors.
 Passing this light
through a prism
does something
different.

Atomic Spectrum
Each element
gives off its own
characteristic
colors.
 Can be used to
identify the atom.
 How we know
what stars are
made of.

• These are called
discontinuous
spectra
• Or line spectra
• unique to each
element.
• These are
emission spectra
• The light is
emitted given off.
Light is a Particle
Energy is quantized.
 Light is energy
 Light must be quantized
 These smallest pieces of light are
called photons.
 Energy and frequency are directly
related.

Energy and frequency
E=hxn
 E is the energy of the photon
 n is the frequency
 h is Planck’s constant
 h = 6.6262 x 10 -34 Joules sec.
 joule is the metric unit of Energy

The Math in Chapter 11
Only 2 equations
 c = ln
 E = hn
 Plug and chug.

Examples
 What
is the wavelength of blue light
with a frequency of 8.3 x 1015 hz?
 What is the frequency of red light
-5
with a wavelength of 4.2 x 10 m?
 What is the energy of a photon of
each of the above?
An explanation of Atomic
Spectra
Where the electron starts
When we write electron
configurations we are writing the
lowest energy.
 The energy level and electron starts
from is called its ground state.

Changing the energy
 Let’s
look at a hydrogen atom
Changing the energy

Heat or electricity or light can move the
electron up energy levels
Changing the energy

As the electron falls back to ground
state it gives the energy back as light
Changing the energy
May fall down in steps
 Each with a different energy

Ultraviolet
Visible
Infrared
 Further they fall, more energy, higher
frequency.
 This is simplified
 the orbitals also have different energies
inside energy levels
 All the electrons can move around.
What is light
Light is a particle - it comes in chunks.
 Light is a wave- we can measure its
wave length and it behaves as a wave
 If we combine E=mc2 , c=ln, E = 1/2
mv2 and E = hn
 We can get l = h/mv
 The wavelength of a particle.

Matter is a Wave
Does not apply to large objects
 Things bigger that an atom
 A baseball has a wavelength of about
10-32 m when moving 30 m/s


An electron at the same speed has a
wavelength of 10-3 cm

Big enough to measure.
The physics of the very small
Quantum mechanics explains how
the very small behaves.
 Classic physics is what you get when
you add up the effects of millions of
packages.
 Quantum mechanics is based on
probability because

Heisenberg Uncertainty
Principle
It is impossible to know exactly the
speed and velocity of a particle.
 The better we know one, the less we
know the other.
 The act of measuring changes the
properties.




More obvious with the very
small
To measure where a electron is, we use
light.
But the light moves the electron
And hitting the electron changes the
frequency of the light.
Before
Photon
Moving
Electron
After
Photon
changes
wavelength
Electron
Changes
velocity