Chapter 4
Arrangement of Electrons
in Atoms
Reference to the best of my knowledge 8-14-11:
Supriya Moore, Monta Vista HS, from
John D. Bookstaver, St. Charles Community College, Cottleville, MO, from
Chemistry, The Central Science, 11th edition
Theodore L. Brown; H. Eugene LeMay, Jr.;
and Bruce E. Bursten (Prentice Hall)
Planck, Bohr, Einstein, deBroglie, Heisenberg,
Schrodinger
• 4.1 The Development of a New Atomic Model
• 4.2 The Quantum Model of the Atom
• 4.3 Electron Configurations
Ch. 3: Democritus, Dalton, Thomson, Millikan, Goldstein, Rutherford, Chadwick
Waves
• To understand the electronic structure of atoms,
one must understand the nature of
electromagnetic radiation.
• The distance between corresponding points on
adjacent waves is the wavelength ().
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Waves
 is Greek letter lambda
 is Greek letter nu
• The number of waves passing a given
point per unit of time is the
frequency ().
• For waves traveling at the same
velocity, the longer the wavelength,
the smaller the frequency.
– Wavelength: It is the distance
between two consecutive peaks
or troughs in a wave.
– Frequency: It indicates how many
waves pass a given point per
second.
– Speed: It indicates how fast a
given peak is moving through the
space.
– Speed of light ,c= ,where
=wave length and  =frequency
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EMR
Electromagnetic Radiation:
Electromagnetic radiation is
one of the ways in which
energy travels through
space. All forms of EMR
compose the
electromagnetic radiation
spectrum, which includes
sun rays, microwaves, Xrays, visible spectrum, UV
rays and IR rays.
• Some characteristics of EMR are:
• All electromagnetic radiation
moves at a constant speed of
about 3.0 X 108 m/s.
• All EMR exhibit wave like
behavior. Waves have three
primary characteristics:
– Wavelength: It is the distance
between two consecutive peaks
or troughs in a wave.
– Frequency: It indicates how
many waves pass a given point
per second.
– Speed: It indicates how fast a
given peak is moving through
the space.
– Speed of light ,c= ,where
=wave length and 
=frequency
Electromagnetic Radiation
• All electromagnetic
radiation travels at the
same velocity: the
speed of light (c),
3.00  108 m/s.
• Therefore,
c = 
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Refer to the following EMR spectrum.
(visible spectrum Roy G. BiV)
• Imagine you have
invented a machine
that allows you to
see all types of EMR.
Make a list of type
of EMR you might
see in your home.
Wave Nature of Light
• Before the concept
of quantization of
energy, the wave
like nature of
light/energy was
widely accepted.
• Two properties that
exhibit the wave
like behavior of
light are
interference and
diffraction.
Animation Diffraction: http://www.acoustics.salford.ac.uk/feschools/waves/diffract3.htm
Animation for Interference:
http://id.mind.net/~zona/mstm/physics/waves/interference/waveInterference1/WaveIn
terference1.html
The Nature of Energy
• The wave nature of light
does not explain how an
object can glow when its
temperature increases.
• Max Planck explained it
by assuming that energy
comes in packets called
quanta.
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Planck’s Theory of Quantization of Energy
• Planck’s theory: Before
Planck’s theory, the wave
model of the light was
widely accepted. But it was
unable to explain some
phenomenon for example
change in the radiation
(wave length) emitted by an
object with the change in
temperature.
h = 6.626 x 10-34 J∙s
• To explain this, Planck
suggested that the energy
transfer or exchange is not a
continuous process, but is
done in small packets of
energy called by him as
quantum.(Word quantum
means fixed amount.) So, he
introduced the concept of
quantization of energy.
• According to Planck’s theory,
E= hv, where
E= energy of radiation
h= Planck’s constant
v= frequency of radiation
Quantization of Energy: Max Plank
• Where else do you
see quantization in
real life?
Therefore, if one knows the wavelength
of light, one can calculate the energy in
one photon, or packet, of that light:
c = 
E = h
The Nature of Energy
Another mystery in
the early 20th century
involved the emission
spectra observed from
energy emitted by
atoms and molecules.
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The Nature of Energy
• Einstein used this assumption
to explain the photoelectric
effect.
• He concluded that
electromagnetic radiation has
a dual wave-particle nature
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Photoelectric Effect: It refers to the emission of electrons from a metal,
when the light shines on the metal. For each metal the frequency of
light needed to release the electrons is different. But the wave theory of
light could not explain it. The photoelectric effect led scientists to think
about the dual nature of light i.e. as a wave and a particle both.
Animation 1:
http://www.upscale.utoronto.ca/GeneralInterest/Harrison/Flash/Nuclear/XRayIntera
ct/XRayInteract.html
Animation 2: http://faculty.ucc.edu/chemistry-pankuch/Photoelectric/PE3.html
Photoelectric Effect
• Max Planck suggested that the
hot object emits energy in small,
specific amounts called quanta.
• 1905, Einstein said
electromagnetic radiation has a
dual wave- particle nature.
• A photon is a particle of
emr having zero rest mass
and carrying a quantum of
energy
• Emr is absorbed onl in
whole numbers of photons,
thus electrons in different
metals require different
minimum frequencies to
exhibit the photoelectric
effect
http://www.shsu.edu/%7Echm_tgc/sounds/flashfiles/pee.s
wf
The Nature of Energy
• For atoms and molecules
one does not observe a
continuous spectrum, as
one gets from a white
light source.
• Only a line spectrum of
discrete wavelengths is
observed.
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Continuous and Line Spectra (Absorption and Emission
Spectrum- Line Spectra)
(http://images.google.com/imgres?imgurl=http://csep10.phys.utk.edu/astr162/lect/light/spectra.gif&imgrefurl=http://csep10.phys.utk.edu/astr162/lect/light/a
bsorption.html&h=240&w=450&sz=33&hl=en&start=2&tbnid=TaN57QO8MhMG4M:&tbnh=66&tbnw=124&prev=/images%3Fq%3Dabsorption%2Band%2Bemission%2Bspectr
um%26svnum%3D10%26hl%3Den%26lr%3D%26sa%3DN)
Bohr Model Of the Hydrogen Atom
• Ephoton=hv
The energy levels of Hydrogen (
As explained by Bohr’s Model) :
•An excited atom (excited state) can
release some or all of its excess
energy by emitting a photon, thus
moving to a lower energy state.
•The lowest possible energy state of
an atom is called the ‘ground state’.
•Different wavelengths of light carry
different amount of energy per
photon. Ex. A beam of red light has
a lower energy photons than beam
of blue light.
The Nature of Energy
•
Niels Bohr adopted Planck’s
assumption and explained
these phenomena in this way:
1. Electrons in an atom can only
occupy certain orbits
(corresponding to certain
energies).
Animation : http://pokok.mysch.net/~chemistry/AL2.htm#Animation
Animation:
http://physics.gac.edu/~chuck/PRENHALL/Chapter%2031/AABXTEJ0.html
© 2009, Prentice-Hall, Inc.
The Nature of Energy
•
Niels Bohr adopted Planck’s
assumption and explained
these phenomena in this way:
2. Electrons in permitted orbits
have specific, “allowed”
energies; these energies will not
be radiated from the atom.
© 2009, Prentice-Hall, Inc.
The Nature of Energy
•
Niels Bohr adopted Planck’s
assumption and explained these
phenomena in this way:
3. Energy is only absorbed or emitted
in such a way as to move an
electron from one “allowed”
energy state to another; the
energy is defined by
E = h
© 2009, Prentice-Hall, Inc.
Light Equations
•
•
•
•
•
c=  
c is the speed of light (3.0
x 108 m/s)
lambda is the wave length
(in m, cm, or nm)
 represents the
frequency (waves/s or
hertz)
http://www.astronomynot
es.com/light/s3.htm
• E=h 
• E is energy (in joules)
• h is Planck’s Constant
(h= 6.626 x 10-34J s)
•  is frequency
• E=h(c/ )
http://sunflower.bio.indiana.edu/~rhangart/courses/b373/lecturenotes/photomorph/sinewave.gif
4.2 The Quantum Model of the Atom
• Louis deBroglie
• Werner Heisenberg
• Based on the photoelectric effect
concept of light behaving as both
a wave and a particle, deBroglie
applied this to electrons, or
quantized energies of Bohr’s
orbits
• Through experimentation,
deBroglie showed the wavelike
property of electrons through
diffraction (bending of a wave)
and interference (waves overlap
resulting in higher or lower
energy)
• Electrons are detected by their
interactions with photons.
Because photons have about the
same energy as electrons, any
attempt to locate a specific
electron with a photon knocks
the electron off its course.
Therefore, the Heisenberg
Uncertainty Principle
• States that it is impossible to
determine simultaneously both
the position and velocity of an
electron or any other particle.
http://hackensackhigh.org/~rkc2/diffraction.jpg
Quantum Theory: Describes mathematically the wave
properties of electrons or other very small particles
treating e- as waves and using Heisenberg’s and De
Broglie’s principles.
Quantum Mechanical Model of Atom (Schrodinger’s Model)
Erwin Schrödinger, in developing a quantum-mechanical model for the
atom, began with a classical equation for the properties of waves. He
modified this equation to take into account the mass of a particle and the de
Broglie relationship between mass and wavelength. The important
consequences of the quantum-mechanical view of atoms are the following:
(http://www.cartage.org.lb/en/themes/sciences/chemistry/Generalchemistry/Atomic/Electronicstructure/Electronicstructures/Quantum/Quantum.htm-)
1.
2.
3.
4.
The energy of electrons in atoms is quantized.
The number of possible energy levels for electrons in atoms of
different elements is a direct consequence of wave-like properties of
electrons.
The position and momentum of an electron cannot both be
determined simultaneously.
The region in space around the nucleus in which an electron is most
probably located is what can be predicted for each electron in an
atom. Electrons of different energies are likely to be found in different
regions. The region in which an electron with a specific energy will
most probably be located is called an atomic orbital.
Quantum Mechanics
• Erwin Schrödinger
developed a mathematical
treatment into which both
the wave and particle
nature of matter could be
incorporated.
• It is known as quantum
mechanics.
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Quantum Mechanics
• The wave equation is
designated with a lower case
Greek psi ().
• The square of the wave
equation, 2, gives a
probability density map of
where an electron has a
certain statistical likelihood of
being at any given instant in
time.
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Quantum Numbers
• Schrodinger arrived at three functions while solving the
wave equation for electrons and came up with three
quantum numbers, each corresponding to a property of
atomic orbital. The fourth quantum number was later
introduced to clarify the spin of electrons.
use(http://www.google.com/search?hl=en&q=wave+mechanical+model)
• Solving the wave equation gives a set of wave
functions, or orbitals, and their corresponding
energies.
• Each orbital describes a spatial distribution of electron
density.
• An orbital is described by a set of three quantum
numbers.
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Principal Quantum Number (n)
• The principal quantum number, n, describes
the energy level on which the orbital resides.
• The values of n are integers ≥ 1.
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Angular Momentum Quantum Number (l)
• This quantum number defines the shape of
the orbital.
• Allowed values of l are integers ranging
from 0 to n − 1.
• We use letter designations to communicate
the different values of l and, therefore, the
shapes and types of orbitals.
Value of l
0
1
2
3
Type of orbital
s
p
d
f
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Magnetic Quantum Number (ml)
• The magnetic quantum number describes
the three-dimensional orientation of the
orbital.
• Allowed values of ml are integers ranging
from -l to l:
−l ≤ ml ≤ l.
• Therefore, on any given energy level, there
can be up to 1 s orbital, 3 p orbitals, 5 d
orbitals, 7 f orbitals, etc.
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Magnetic Quantum Number (ml)
• Orbitals with the same value of n form a shell.
• Different orbital types within a shell are subshells.
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Orbitals and Electron Capacity of the First Four Principle Energy
Levels
Maximum
Principle
Number of Number of
Type of
number of
energy level
orbitals per orbitals per
sublevel
electrons
(n)
type
level(n2)
(2n2)
1
2
3
4
s
1
s
1
p
3
s
1
p
3
d
5
s
1
p
3
d
5
f
7
1
2
4
8
9
18
16
32
s Orbitals
• The value of l for s
orbitals is 0.
• They are spherical in
shape.
• The radius of the sphere
increases with the value
of n.
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s Orbitals
Observing a graph of
probabilities of finding an
electron versus distance
from the nucleus, we see
that s orbitals possess
n−1 nodes, or regions
where there is 0
probability of finding an
electron.
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p Orbitals
• The value of l for p orbitals is 1.
• They have two lobes with a node between them.
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d Orbitals
• The value of l for a d
orbital is 2.
• Four of the five d
orbitals have 4
lobes; the other
resembles a p
orbital with a
doughnut around
the center.
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Energies of Orbitals
• For a one-electron
hydrogen atom,
orbitals on the same
energy level have the
same energy.
• That is, they are
degenerate.
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Energies of Orbitals
• As the number of
electrons increases,
though, so does the
repulsion between
them.
• Therefore, in manyelectron atoms, orbitals
on the same energy
level are no longer
degenerate.
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Spin Quantum Number, ms
• In the 1920s, it was
discovered that two
electrons in the same
orbital do not have exactly
the same energy.
• The “spin” of an electron
describes its magnetic
field, which affects its
energy.
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Spin Quantum Number, ms
• This led to a fourth
quantum number, the spin
quantum number, ms.
• The spin quantum number
has only 2 allowed values:
+1/2 and −1/2.
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Pauli Exclusion Principle
• No two electrons in the
same atom can have
exactly the same energy.
• Therefore, no two
electrons in the same atom
can have identical sets of
quantum numbers.
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5.2
Electron Configurations
According to the
aufbau principle,
electrons occupy
the orbitals of
lowest energy
first.
According to the Pauli
exclusion principle, an atomic
orbital may describe at most
two electrons. To occupy the
same orbital, two electrons
must have opposite spins
Hund’s rule states that electrons
occupy orbitals of the same energy
in a way that makes the number of
electrons with the same spin
direction as large as possible.
Electron Configurations
• This shows the
distribution of all
electrons in an atom.
• Each component consists
of
– A number denoting the
energy level,
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Electron Configurations
• This shows the
distribution of all
electrons in an atom
• Each component consists
of
– A number denoting the
energy level,
– A letter denoting the type
of orbital,
Animation: http://intro.chem.okstate.edu/WorkshopFolder/Electronconfnew.html
© 2009, Prentice-Hall, Inc.
Electron Configurations
• This shows the
distribution of all
electrons in an atom.
• Each component consists
of
– A number denoting the
energy level,
– A letter denoting the type
of orbital,
– A superscript denoting the
number of electrons in
those orbitals.
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Orbital Diagrams
• Each box in the diagram
represents one orbital.
• Half-arrows represent the
electrons.
• The direction of the
arrow represents the
relative spin of the
electron.
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Hund’s Rule
“For degenerate
orbitals, the lowest
energy is attained
when the number of
electrons with the
same spin is
maximized.”
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Periodic Table
• We fill orbitals in
increasing order of
energy.
• Different blocks on the
periodic table (shaded in
different colors in this
chart) correspond to
different types of
orbitals.
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Some Anomalies
Some irregularities
occur when there
are enough
electrons to half-fill
s and d orbitals on
a given row.
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Some Anomalies
For instance, the
electron
configuration for
copper is
[Ar] 4s1 3d5
rather than the
expected
[Ar] 4s2 3d4.
© 2009, Prentice-Hall, Inc.
Some Anomalies
• This occurs
because the 4s and
3d orbitals are very
close in energy.
• These anomalies
occur in f-block
atoms, as well.
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5.2
Exceptional Electron Configurations
Why do actual electron configurations for some
elements differ from those assigned using the
aufbau principle?
– Some actual electron configurations differ from those
assigned using the aufbau principle because half-filled
sublevels are not as stable as filled sublevels, but they
are more stable than other configurations.
– Exceptions to the aufbau principle are due to
subtle electron-electron interactions in orbitals
with very similar energies.
– Copper has an electron configuration that is an
exception to the aufbau principle.
It is
1s22s22p63s23p64s13d10
Instead of
1s22s22p63s23p64s23d9
http://www.tannerm.com/Quick_atom/hund.gif
Electron Configuration Theories
• Aufbau’s Principle: An
electron occupies the
lowest-energy orbital that
can receive it.
• Pauli’s Exclusion Principle:
No two electrons in the
same atom can have the
same set of four quantum
numbers.
• Hund’s Rule: Orbitals of
equal energy are each
occupied by one electron
before any orbital is
occupied by a second
electron, and all electrons
in singly occupied orbitals
must have the same spin.
Aufbau principle:
Lowest energies first
1s, 2s, 2p, 3s, 3p, 4s
3d, 4p, 5s
It follows the periodic
table
Electron Configurations in Groups
Group 1A elements -- there
is only one electron in the
highest occupied energy
level.
Group 4A elements -there are four
electrons in the
highest occupied
energy level.
noble gases
are the
elements in
Group 8A
Electron Configuration and Orbital
Filling Practice
Write the electron
a. Li: atomic number 3
configuration and orbital
filling for
1s22s1
 _ 
a. Li
b. Mg
b. Mg: atomic number 12 1s22s22p63s2
c. Si
 _  _ _ 
c. Si: atomic number 14
1s22s22p63s23p2
 _  _ _  _ 
Ways to Represent Electron Configuration
1. Expanded Electron Configuration
2. Condensed Electron Configurations
3. Orbital Notation
4. Electron Dot Structure
Write the above four electron configurations for
a) oxygen
b) zinc
c) zinc ion
d) cu ion.
Quantum Number Terms
• Ground State: Lowest energy
state of an atom
• Excited State: A state in which
an atom has a higher potential
energy then it has in its ground
state
• Orbital: A 3D region around the
nucleus that indicates the
probable location of an
electron
• Quantum Numbers: Specify
the properties of atomic
orbitals and the properties of
electrons in orbitals
• Principle Quantum Number:
(n) Indicates the main energy
level occupied by the electron.
• Angular Momentum Quantum
Number: (l) Indicates the shape
of the orbital.
• Magnetic Quantum Number:
(m) Indicates the orientation of
an orbital around the nucleus.
• Spin Quantum Number: (+1/2,
-1/2) Indicates the two
fundamental spin states of an
electron in an orbital
Chapter 4 Objectives
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
Explain the mathematical relationship between the speed, wavelength and frequency of
electromagnetic radiation (problems)
Know that X rays, gamma rays and UV rays have short wavelength and high energy, radio waves
have long wavelength and low energy
Discuss the dual wave-particle nature of light
Discuss the significance of the photoelectric effect and the line emission spectrum of hydrogen
to the development of the atomic model
Describe the Bohr model of the hydrogen atom, draw the Bohr model and label the parts
Compare and contrast Thompson, Rutherford and the Bohr models (at least three similarities
and three differences)
Discuss Louis de Broglie’s role in the development of the quantum model of the atom
Compare and contrast the Bohr model and the quantum model of the atom
State Heisenberg uncertainty principle
Explain how Heisenberg uncertainty principle and the Schroedinger wave equation led to the
idea of atomic orbitals
List the four quantum numbers and describe their significance
Relate the number of sublevels corresponding to each of an atom’s main energy level, the
number of orbitals per sublevel and the number of orbitals per main energy level
List the total number of electrons needed to fully occupy each main energy level
State the Aufbau principle, the Pauli exclusion principle and Hund’s rule
Write electron configurations for elements on the chapter 1 packet list using orbital notation,
electron configuration notation and noble gas notation
Explain why the electron configurations of chromium and copper do not follow Aufbau’s
principle?