Chapter 5
“Electrons in Atoms”
Ernest Rutherford’s Model
• Discovered dense + piece at
nucleus
• Electrons move around it, like
planets around sun
• Mostly empty space
• Didn’t explain chemical
properties of elements
Niels Bohr’s Model
• Why don’t electrons fall into nucleus?
• Move like planets around sun.
specific circular orbits at different
levels.
An amount of fixed energy separates
one level from another.
The Bohr Model of the Atom
I pictured the
electrons orbiting
the nucleus much
like planets
orbiting the sun.
Niels Bohr
However, electrons
are found in
specific circular
paths around the
nucleus, and can
jump from one
level to another.
Bohr’s model
• Energy level measure of fixed
energy e- can have
•Like rungs of ladder
• e- can’t exist between energy
levels
• can’t stand between rungs on
ladder
• Unlike ladder, energy levels not
evenly spaced
• Higher energy levels closer together
– less energy needed for jump
The Quantum Mechanical Model
• Energy is “quantized” - in chunks.
• A quantum is exact energy needed to
move e- one energy level to another.
• Since energy of atom is never “in
between” quantum leap in energy
must exist.
• Erwin Schrodinger (1926) derived
equation described energy and
position of e- in an atom
Schrodinger
The Quantum Mechanical Model
• Very small things behave
differently from big things
• quantum mechanical model
is a mathematical solution
• not like anything you can
see (like plum pudding!)
The Quantum Mechanical
Model
• Has energy levels for e
• Orbits not circular.
• only tells us probability of finding e a
certain distance from nucleus.
The Quantum Mechanical Model
• e- found inside blurry
“electron cloud” (area
where there’s chance
of finding e• Like fan blades or
bicycle wheel
Atomic Orbitals
• Principal Quantum Number (n) = the
energy level of e- (1, 2, 3, etc.)
• Within each energy level, Schrodinger’s
equation describes several shapes.
• called atomic orbitals - regions of space w/
high probability of finding e• Sublevels like rooms in a hotel
• letters s, p, d, and f
Principal Quantum Number (n)
denotes the energy level (shell) e- is
located.
Maximum number
of e- that can fit in
energy level is:
2n2
How many e- in level 2?
level 3?
Individual orbitals
# of
orbitals
s
spherical
p
dumbell
d
1
2
1st
3
2nd
5
6
10
7
14
4th
clover leaf
f
complicated
Maximum
electrons
First
possible
energy level
3rd
By Energy Level
• Energy Level 1 (n=1)
• Has only s sublevel
2
• 1s (1 orbital)
• w/ only 2 e• 2 total e-
• Energy Level 2 (n=2)
• Has s and p
sublevels available
• 2s 2 (1 orbital)
• w/ 2 e6
• 2p (3 orbitals)
• w/ 6 e• 2s22p6
• 8 total e-
By Energy Level • Energy level 4 (n=4)
• Energy level 3 (n=3)
• s, p, and d sublevels
2
• 3s
(1 orbital)
• w/ 2 e6
• 3p
(3 orbitals)
• w/ 6 e10
• 3d
(5 orbitals)
• w/ 10 e2
6
10
• 3s 3p 3d
• 18 total e-
• s, p, d, and f sublevels
• 4s 2 (1 orbital)
• w/ 2 e• 4p6
(3 orbitals)
• w/ 6 e10
• 4d
(5 orbitals)
• w/ 10 e• 4f 14 (7 orbitals)
• w/ 14 e• 4s24p64d104f14
• 32 total e-
By Energy Level
Any more than
the fourth and not
all orbitals fill up.
• You simply run out
of e-’s
s and p orbitals 1:20
d orbitals 3:40
• orbitals do not fill
up in neat order.
• energy levels
overlap
• Lowest energy fill
first.
Summary of Principal Energy Levels, Sublevels, and
Orbitals
Principal Number
energy
of
level
sublevels
n=1
1
n=2
2
n=3
3
n=4
4
Type of
sublevel
1s (1 orbital)
2s (1 orbital
2p (3 orbitals)
3s (1 orbital)
3p (3 orbitals)
3d (5 orbitals)
4s (1 orbital)
4p (3 orbitals)
4d (5 orbitals)
4f (7 orbitals)
Max # of
Electron
electrons configuration
2
8
18
32
1s2
2s2
2p6
3s2
3p6
3d10
4s2
4p6
4d10
4f14
Electron distribution in an Atom
3d
3p
Energy
Level
3
ENERGY
3s
2p
2
2s
1
1s
NUCLEUS
Section 5.2
Electron Arrangement in Atoms
• OBJECTIVES:
•Describe how to write the
electron configuration for an
atom.
Section 5.2
Electron Arrangement in Atoms
• OBJECTIVES:
•Explain why the actual electron
configurations for some elements
differ from those predicted by
the aufbau principle.
Increasing energy
7s
6s
5s
7p
6p
5p
4p
4s
6d
5d
4d
5f
4f
3d
3p
3s
2p
2s
1s
aufbau diagram - page 133
Aufbau is German for “building up”
Electron Configurations…
•
…the way electrons arranged in various
orbitals around nuclei of atoms. Three
rules tell us how:
1) Aufbau principle - electrons enter the
lowest energy first.
• causes difficulties b/c overlap of orbitals
of different energies – follow diagram!
2) Pauli Exclusion Principle - 2 electrons max
per orbital (hotel room) - different spins
Pauli Exclusion Principle
No two electrons in an
atom can have the same
four quantum numbers.
To show the different
direction of spin, a pair
in the same orbital is
written as:
Wolfgang Pauli
Quantum Numbers
Each electron in an atom has a
unique set of 4 quantum numbers
which describe it.
1)
2)
3)
4)
Principal quantum number
Angular momentum quantum number
Magnetic quantum number
Spin quantum number
Electron Configurations
3) Hund’s Rule- When electrons occupy
orbitals of equal energy, they don’t
pair up until they have to.
• write e- configuration for
Phosphorus
 We need to account for all 15 e-’s
in phosphorus
Increasing energy
7s
6s
5s
4s
3s
2s
1s
7p
6p
5p
4p
6d
5d
4d
3d
3p • The first two electrons
go into the 1s orbital
2p
Notice the opposite
direction of the spins
• only 13 more to go...
5f
4f
Increasing energy
7s
6s
5s
7p
6p
5p
4p
4s
6d
5d
4d
5f
4f
3d
3p
3s
2p
2s
1s
• The next electrons go
into the 2s orbital
Increasing energy
7s
6s
5s
7p
6p
5p
4p
4s
6d
5d
4d
5f
4f
3d
3p
3s
2p
2s
1s
• The next electrons
go into the 2p orbital
• only 5 more...
Increasing energy
7s
6s
5s
7p
6p
5p
4p
4s
6d
5d
4d
5f
4f
3d
3p
3s
2p
2s
1s
• The next electrons
go into the 3s orbital
• only 3 more...
Increasing energy
7s
6s
5s
4s
3s
2s
1s
7p
6p
5p
4p
6d
5d
4d
5f
4f
3d
3p • The last three electrons
go into the 3p orbitals.
2p They each go into
separate shapes (Hund’s)
• 3 unpaired electrons
Orbital
notation
= 1s22s22p63s23p3
Stairstep pattern
• An internet program about electron configurations is:
Electron Configurations
(Just click on the above link)
I
electron config 3:24
Orbitals fill in an order
• Lowest energy  higher energy.
• Adding e-’s changes energy of
orbital. Full orbitals are best
situation.
• half filled orbitals  lower energy,
next best
•more stable.
•Changes filling order
Write the electron configurations for
these elements:
• Titanium - 22 electrons
2 2 6 2 6 2 2
 1s 2s 2p 3s 3p 4s 3d
• Vanadium - 23 electrons
2 2 6 2 6 2 3
 1s 2s 2p 3s 3p 4s 3d
• Chromium - 24 electrons
2 2 6 2 6 2 4 (expected)
 1s 2s 2p 3s 3p 4s 3d
But this is not what happens!!
Chromium is actually:
• 1s22s22p63s23p64s13d5
• Why?
• This gives us two half filled orbitals
(the others are all still full)
• Half full is slightly lower in energy.
• The same principal applies to copper.
Copper’s electron configuration
• Copper has 29 electrons so we expect:
1s22s22p63s23p63d94s2
• But the actual configuration is:
• 1s22s22p63s23p63d104s1
• This change gives one more filled orbital
and one that is half filled.
• Remember these exceptions: d4, d9
Irregular configurations of Cr and Cu
Chromium steals a 4s electron to
make its 3d sublevel HALF FULL
Copper steals a 4s electron
to FILL its 3d sublevel
Section 5.3
Physics and the Quantum
Mechanical Model
• OBJECTIVES:
•Describe the relationship
between the wavelength
and frequency of light.
Section 5.3
Physics and the Quantum
Mechanical Model
• OBJECTIVES:
•Identify the source of
atomic emission spectra.
Section 5.3
Physics and the Quantum
Mechanical Model
• OBJECTIVES:
•Explain how the frequencies
of emitted light are related to
changes in electron energies.
Section 5.3
Physics and the Quantum
Mechanical Model
• OBJECTIVES:
•Distinguish between
quantum mechanics and
classical mechanics.
Light
• Study of light led to development of quantum
mechanical model.
• Light is electromagnetic radiation.
• EM radiation: gamma rays, x-rays, radio
waves, microwaves
• Speed of light = 2.998 x 108 m/s
• abbreviated “c”
• “celeritas“ Latin for speed
• All EM radiation travels same in vacuum
- Page 139
“R O Y
Frequency Increases
Wavelength Longer
G
B I V”
Parts of a wave
Crest
Wavelength
Amplitude
Origin
Trough
Electromagnetic radiation propagates through
space as a wave moving at the speed of light.
Equation:
c =
c = speed of light, a constant (2.998 x 108 m/s)
 (lambda) = wavelength, in meters
 (nu) = frequency, in units of hertz (hz or sec-1)
Wavelength and Frequency
• inversely related
•one gets bigger, other smaller
• Different frequencies of light different
colors
• wide variety of frequencies (spectrum)
- Page 140
Use Equation: c =
Low
Energy
High
Energy
Radio Micro Infrared
Ultra- XGamma
waves waves .
violet Rays Rays
Low
High
Frequency
Frequency
Long
Short
Wavelength
Visible Light Wavelength
Long
Wavelength
=
Low Frequency
=
Low ENERGY
Short
Wavelength
=
High Frequency
=
High ENERGY
Atomic Spectra
• White light all
colors of visible
spectrum.
• prism separates
it.
If the light is not white
• heating gas with
electricity will emit
colors.
• Passing this light
through prism
different.
Atomic Spectrum
• Each element gives
off own
characteristic
colors.
• This is how we
know composition
of stars
• atomic emission
spectrum
• Unique to each
element, like
fingerprints!
• ID’s elements
Light is a Particle?
• Energy is quantized.
• Light is energy…..
• light must be quantized
• photons smallest pieces of light
• Photoelectric effect –
• Matter emits e- when it absorbs energy
• Albert Einstein Nobel Prize in chem
• Energy & frequency: directly related.
energy (E ) of electromagnetic radiation is
directly proportional to frequency () of
radiation.
Planck-Einstein Equation:
E = h
E = Energy, in units of Joules (kg·m2/s2)
(Joule is metric unit of energy)
h = Planck’s constant (6.626 x 10-34 J·s)
(reflecting sizes of energy quanta)
 = frequency, in units of hertz (hz, sec-1)
The Math in Chapter 5
•
There are 2 equations:
1) c = 
2) E = h
Put these on your 3 x 5 notecard!
Examples
1) What is the wavelength of blue
light with a frequency of 8.3 x 1015
hz?
2) What is the frequency of red light
with a wavelength of 4.2 x 10-5 m?
3) What is the energy of a photon of
each of the above?
Explanation of atomic spectra
• electron configurations written in
lowest energy.
• energy level, and where electron
starts from, called it’s ground state
- lowest energy level.
Changing the energy
• Let’s look at a hydrogen atom, with only
one electron, and in the first energy
level.
Changing the energy
• Heat, electricity, or light can move electron
up to different energy levels. The electron
is now said to be “excited”
Changing the energy
• As electron falls back to ground state, it
gives energy back as light
Experiment #6, page 49-
Changing the energy
• may fall down in specific steps
• Each step has different energy
Lyman series (UV)
Balmer series
(visible)
Paschen series
(infrared)
Ultraviolet
Visible
Infrared
• further they fall, more energy released =
higher frequency
• orbitals also have different energies
inside energy levels
• All electrons can move around.
What is light?
• Light is a particle - it comes in chunks.
• Light is a wave - we can measure its wavelength
and it behaves as a wave
• combine E=mc2 , c=, E = 1/2 mv2 and E = h,
then we can get:
= h/mv
(from Louis de Broglie)
Calculates wavelength of a particle.
• called de Broglie’s equation
• He said particles exhibit properties of waves
Wave-Particle Duality
J.J. Thomson won the Nobel prize for describing the
electron as a particle.
His son, George Thomson won the Nobel prize for
describing the wave-like nature of the electron.
The
electron is
a particle!
The electron
is an energy
wave!
Confused? You’ve Got Company!
“No familiar conceptions can be
woven around the electron;
something unknown is doing we
don’t know what.”
Physicist Sir Arthur Eddington
The Nature of the Physical World
1934
The physics of the very small
• Quantum mechanics explains how
very small particles behave
•Quantum mechanics is an
explanation for subatomic
particles and atoms as waves
• Classical mechanics describes the
motions of bodies much larger than
atoms
Heisenberg Uncertainty
Principle
• impossible to know exact location and
velocity of particle
• better we know one, less we know
other
• Measuring changes properties.
• True in quantum mechanics, but not
classical mechanics
Heisenberg Uncertainty Principle
“One cannot simultaneously
determine both the position
and momentum of an
electron.”
Werner Heisenberg
You can find out where the
electron is, but not where it is
going.
OR…
You can find out where the
electron is going, but not where
it is!
It is more obvious with the very
small objects
•To measure where e-, we use
light
•But light energy (photon) moves
e- due to small mass
•And hitting e- changes frequency
of light
After
Before
Photon
Moving
Electron
Photon
wavelength
changes
Electron
velocity changes
Fig. 5.16, p. 145