Chemistry, The Central Science, 10th edition
Theodore L. Brown; H. Eugene LeMay, Jr.; and Bruce E. Bursten
Chapter 6
Electronic Structure
of Atoms
John D. Bookstaver
St. Charles Community College
St. Peters, MO
 2006, Prentice Hall, Inc.
6.1
The Wave Nature of
Light
Ch. 6
Reading Guide
Section 6.1:
1) Define EM radiation and list its properties
A form of radiation that has wave
characteristics and that propagates through a
vacuum at the characteristic speed of 3.00 x
108 m/s or…
• 1) carries energy through space
• 2) moves through a vacuum at the speed of light
• 3) have wave-like characteristics
2) Define the properties & parts of a wave
(λ) Wavelength – distance between 2
adjacent peeks
Amplitude – vertical distance from the midline
(aka: origin) of the wave to its crest/trough
(ѵ) Frequency – the # of complete
wavelengths or cycles that pass a given point
each second
3) What is the speed of light? Formula???
c = 3.00 x 108 m/s
c = ѵλ (speed of light equation)
Inverse relationship between λ and ѵ:
• The shorter the
wavelength, the
higher the frequency
and vice versa
 Units:
Short  = High 
Long  = Low 
• Frequency – given in cycles/second or Hertz (Hz) or s–1
• Wavelength - depends on type of radiation (see #4)
4) Table 6.1: Units & Types of Radiation
Unit
Symbol
Type of Radiation
Ӑ
Length
(meters)
10-10
Angstrom
Nanometer
nm
10-9
ultraviolet, visible
Micrometer
μm
10-6
infrared
Millimeter
mm
10-3
infrared
Centimeter
cm
10-2
microwave
Meter
m
1
TV, radio
x-ray
* Gamma rays can be similar in length to the
diameter of an atom vs. radio waves which can be
as long as a football field
The Electromagnetic Spectrum
Electronic
Structure
of Atoms
6.2
Quantized Energy
and Photons
Section 6.2:
1) What is the relationship between
hot objects and quantized energy?
When solids are heated they emit radiation
• (ex: red glow of an electric stove burner)
The wavelength distribution (and thus color) of the
radiation depends on temperature (
• ex: a red-hot object is cooler than a white-hot one)
Max Planck assumed that energy could either be
absorbed or released by atoms only in discrete
“chunks” which he called quantums (meaning “fixed
amount”)
2) Explain the relationship between a
quantum of energy and Planck’s constant.
The energy (E) of a single quantum = a constant
multiplied by the frequency of radiation
• E = hѵ where h (Planck’s constant)= 6.63 x 10-34 J•s
• Matter is allowed to emit and absorb energy only in
whole number multiples of hѵ; energy can only be
released in specific amounts so the energy is
considered “quantized” (Ex: potential energy of a
person walking up ramp vs. stairs)
Staircase Analogy:
each step requires an exact amount of
energy and distance be traveled; there
is no in-between so each step is a
“quantized” amount of energy
Electronic
Structure
of Atoms
3) Explain the photoelectric effect (PEE) and
role of photons
 Photoelectric effect = the observation made by Einstein
that many metal surfaces emit electrons when light shines
upon them
• Each metal has a minimum frequency of light, below
which, no electron are emitted from the atoms
• The light striking the metal behaves like a stream of tiny
energy packets/particles
– Significance: until Einstein observed the PEE, light was
believed ONLY to travel in WAVES, however the PEE suggests
that light must also be able to travel as small packets of energy
called photons (energy of a photon is distinct: E = hѵ)
• 3 possible PEE situations:
– 1) photon w/ low energy = no electrons escape
– 2) photon w/ sufficient energy = electrons are emitted
– 3) photon w/extra energy =electrons emitted w/more speed(KE)
Photoelectric Effect (continued)
http://phet.colorado.edu/en/simulation/photoelectric
• High ѵ and E = electrons emitted
If ѵ and E are not at least
the minimum value for the
metal, it doesn’t matter
how high the intensity
(brightness) of light it b/c
each photon packet/
particle only has a
quantized amount of E to
knock out an electron with
• Low ѵ and E = no electrons
4) Why is light (EM radiation) described as
having both wave-like and particle-like
characteristics?
 In certain situations, light behaves more like a wave, but in
other situations (like w/ Einstein’s theory of light as a
stream of photon particles producing the PEE) it behaves
more like particles
 In March 1905 , Einstein created the quantum theory of
light, the idea that light exists as tiny packets, or particles,
which he called photons. Alongside Max Planck's work on
quanta of heat Einstein proposed one of the most shocking
idea in twentieth century physics: we live in a quantum
universe, one built out of tiny, discrete chunks of energy
and matter
http://www.olympusmicro.com/primer/lightandcolor/particleorwave.html
6.3
Line Spectra +
Bohr Model
Section 6.3:
1) Explain the concept of radiation as it relates to λ,
E, and spectrum (continuous vs. line spectra)
 Common radiation sources (light bulbs, stars) contain many
different wavelengths of light; when radiation from a source
like this is separated into it’s different λ components a
spectrum is produced
• Continuous Spectrum – contains radiation of all
wavelengths and appears as a continuous rainbow (ex:
raindrops of mist act as a prism for sunlight)
– White light + prism = CONTINUOUS SPECTRA
• Line Spectrum – contains radiation of only a few specific
wavelengths (ex: gases excited by an electrical charge)
– Colored light + prism = LINE SPECTRA
Line Spectra
• When electric current is passed through
pressurized gases in a tube, the gases
emit different colors of light
(ex: sodium is yellow, neon is red-orange)
 When this colored light is passed through a prism, the
result is a line spectra containing only a few specific
wavelengths
 Every gas has a unique line spectra, often referred to
as the gas’s
“fingerprint”
Electronic
Structure
of Atoms
2) Identify 3 postulates that are the basis of
Bohr’s model of electron orbitals.
1) Only orbits of certain radii (size), corresponding
to certain definite energies, are permitted for the
electron in a hydrogen atom.
2) An electron in a permitted orbit has a specific
energy and is in an “allowed” energy state. An
electron in an allowed energy state will not radiate
energy and therefore will not spiral into the nucleus.
3) Energy is emitted or absorbed by the electron
only as the electron changes from one allowed
energy state to another. This energy is emitted or
absorbed as a photon (E = hѵ).
3) What is the principal quantum number (n)?
 Niels Bohr assumed e– moved
around the nucleus in distinct
circular paths called orbits
(aka: planetary model)
• Each orbit around the nucleus has
a different “n” value (known as the
principle quantum number)
o n = 1 is the closest to the nucleus;
and as the value of “n” increases,
the orbits get farther away from
the nucleus
o As “n” increases, the radius size
of the orbit gets larger, the energy
of the e– in the orbit increases,
and the atom becomes less stable
Bohr Model of
the Atom
* The Bohr model offers
an explanation for the
line spectra of the
hydrogen atom only; it
accounts for other atoms
in a crude way
4) Explain the relationship between ground
state & excited state electrons
Like Planck, Bohr also believed energy was
quantized; each orbit in the atom has a specific
quantity of energy which increases as the value of
“n” increases
• Ground state – lowest energy state (n = 1) that
an electron can occupy in an atom
• Excited state – when an electron is in a higher
energy orbit (n = 2 or higher)
Electron “Jumping” in the atom
 According to Bohr, electrons can “jump” between
energy levels ONLY if the exact amount of energy
needed was gained or lost by the e– (ex: like rungs
on a ladder)
 e– demotion: e– moving from
higher  lower orbits/“n” will emit
radiant energy (energy released)
 e– promotion: e– moving from
lower  higher orbits/“n” will absorb
radiant energy (energy required)
The color of the
firework depends
on how many e- are
in the atoms and
which energy level
these electrons are
located in…
The energy emitted
as the e- are
demoted depends
on the energy level
transitions and
gives off a distinct λ
and color
This is what happens in fireworks…
the e- are excited by heating and are
promoted (becoming less stable).
Almost immediately, the e- emit
radiation in order to be demoted to a
lower, more stable energy level
Electronic
Structure
of Atoms
The Rydberg Equation
The energy absorbed or emitted
(ΔE) from the process of electron
“jumping” can be calculated by
the equation:
E = −RH
(
1
1
- 2
2
ni
nf
• RH = Rydberg constant =
2.18  10−18 J
• ni and nf = initial and final
energy levels of the e–
 e– demotion = - ΔE
 e– promotion = + ΔE
)
Explanation - Line Emission Spectra
•
The specific spectral lines seen when an gas’s
radiant energy is separated through a prism
can mathematically be related to the Rydberg
equation
 Thus, the existence of these spectral lines is due to
the quantized jumps made by e– between energy
levels
 Since each element has a different # of e– (in
different energy levels), the energy of each “jump”
in the atom will be different from different elements,
resulting in unique  (and colors) for every element
= unique line emission spectra!!!
5) What were the most significant contributions
of Bohr’s model to our current understanding of
electron structure?
1) electrons exist only in certain discrete energy
levels which are described by quantum numbers
2) energy is involved in moving an electron from
one level to another
----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
Limitations of Bohr Model:
• 1) Only offers explanation for line spectra of Hydrogen
because it only has 1 e- (his model only crudely explains
other elements)
• 2) Bohr model only views the electron as a particle and
ignores the wavelike properties that exist
6.4
The Wave Behavior
of Matter
Section 6.4:
1) What is meant by the term “matter waves”,
especially as it applies to e- and what is the
equation to describe this property?
 Matter Waves: describes the wave-like characteristics of
material particles
• (Louis de Broglie theorized that, if light waves can act like particles
(from Einstein & PEE) then why can’t matter particles (like e-) behave
like waves???)
 de Broglie Equation: as e- move around the nucleus, the emovement can be interpreted as a wave and has a
wavelength relative to its
= h
mass (m) and velocity (v)
mv
• Only very small objects are in the range of observation
Proof of de Broglie Theory
• A few years after his proposed theory,
experimental results backed de Broglie
Electrons passed through a solid crystal and were
diffracted (broken up around slits just like a beam of
light)
The double-slit experiment, demonstrates that
matter and energy can display characteristics of
both waves and particles
This technique leads to the development of the
electron scanning microscope
http://www.youtube.com/watch?v=MTuyEn-ngIQ
Chicken Embryo; Termite; Dust Mite; Spider
Electronic
Structure
of Atoms
2) Explain the Heisenberg Uncertainty Principle
as it applies to e- (no equation needed)
 The dual nature of matter places a fundamental
limitation on how accurately both the speed and
position of an object can be known
 This limitation becomes important only when matter is of
subatomic size
 It is inherently impossible for us to simultaneously
known BOTH the exact momentum of the e- and its
exact location in space with any great degree of
certainty
 Now, recent models precisely describe the energy
of an electron, but describe its location in terms of
probabilities (likelihood of finding an e- in a region
of the atom)
Electronic
Structure
of Atoms
Bohr’s Model… incorrect
• Why does the Bohr model of the atom violate
the uncertainty principle?
• Bohr  thought e– traveled in orbits
this cannot be true, b/c then the exact path
and position of an e– would be known at all
times
• De Broglie’s hypothesis and Heisenberg's
uncertainty principle set the stage for a new
model of the atom
Recognizes the wave nature of e– and the
distinct energy levels that Bohr founded to
describe the probable location of an e–
Quiz Review: 6.1 – 6.4
• List all 7 types of radiation on the EM Spectrum in
order of increasing frequency.
 Radio, Microwaves, IR, Visible, UV, X-rays, Gamma rays
indirect
• There is a(n) ____________
relationship between
wavelength and frequency.
directly
• Energy and frequency are _____________
proportional to one another, meaning as one
increases
increases, the other _____________.
• The units for:
Hz = s-1
 Frequency: _______________
m or nm
 Wavlength: _______________
 Energy: ______________
J
Quiz Review: 6.1 – 6.4
• Important equations and constants will be given

 E = h
 c=
E = −RH
(
1
nf2
-
1
ni 2
)
[Rydberg]
 E = hc = h

•
•
•
Continuous spectra vs. line spectra
Photoelectric effect – Einstein proved that waves behaved as particles
Bohr model of the atom
 Energy levels/orbits, ground state vs. excited state
 Useful parts of the Bohr model?
•
•
Absorbtion/Emissison of energy & electron jumping (relationship to quantized
energy
Heisenberg’s Uncertainty Principle – how does Bohr’s model violate this
principle?
6.5
Quantum Mechanics
& Atomic Orbitals
Quantum Mechanics
• In 1926, Erwin Schrödinger developed an equation
(Schrodinger’s wave equation), which incorporated
both the wave and particle natures of matter
• This new way of dealing with subatomic particles
is known as quantum mechanics.
Quantum Mechanical Model
• The next atomic model, The Quantum
Mechanical Model, took Bohr’s idea
about electrons existing in separate
energy levels …
 What was different about this model?
• Applies Heisenberg’s uncertainty
principle and the distinct energy
levels that e- travel in from Bohr’s
model
• The quantum mechanical model
of the atom statistically describes
a general region of space around
the nucleus where an electron is
likely to be found at any given
instant
Quantum Mechanical Model
• Define energy level –
Designates the main energy
shell around the nucleus where
the electron is likely to be found
1) Electrons can “jump” from one
energy level to another
2) Electrons cannot exist
between energy levels
3) The higher the energy level,
the further the electron is from
the nucleus
Quantum Mechanical Model
4) Energy levels are not equal distances from one
another (they become more closely spaced, and
closer in energy, the further they are from the
nucleus)
5) The higher the energy level occupied by an
electron, the easier it is for the electron to
escape
Quantum Mechanical Model
shells
subshells
orbitals
- principal energy
level
- s,p,d,f within each
energy level
- Very specific
orientation of
subshells
electrons
• Define atomic orbital:
 Specific region of space within a designated subshell in
which an electron is likely to be found
Quantum Mechanical Model
s orbitals – spherical
p orbitals – dumbbell shaped
d orbitals – 4-leaf clover & dumbbell w/donut
f orbitals – very complicated!
2
8
18
32
s
s, p
s, p, d
s, p, d, f
“s” orbital shape
• Lowest energy
orbitals
• Spherical in shape
• Radius of sphere
increases with
increasing value of n
“p” orbital shape
 There are three dumbbell-shaped p orbitals
beginning in the 2nd energy level (n=2) and above
“d” orbital shapes
 There are 5 orbitals
for each d subshell
beginning in the 3rd
energy level (n=3)
and above
• 4 of them have 4
lobes like “fourleaf clovers”
• the 5th
resembles a p
orbital with a
doughnut around
the center.
Shape of “f” orbitals
Turn to packet pg. 3
Energy Level
Diagram
 Degenerate orbitals
are all of EQUAL
energy
 As energy increases,
the difference
between the
energies of the
orbitals become less
and less pronounced
 What makes an atom
stable?
• 1) e- in lower
energy orbitals
• 2) having FULL or
HALF-FULL
orbitals
Electronic
Structure
of Atoms
Quantum Numbers
• Mathematically solving the wave equation
gives a set of wave functions (aka: orbitals)
and their corresponding energies.
• Each orbital …
describes the distribution of electron
density in space.
has a characteristic energy & shape
• An orbital is described by a set of three
quantum numbers.
Principal Quantum Number, n
• Also seen in Bohr model, this quantum
number describes the energy level in
which the orbital resides.
• n values are positive integers (starting at 1)
• As n increases…
 the orbital become larger
 e– spend more time further from the
nucleus
 e– have a higher energy
Azimuthal Quantum Number, l
• This quantum number defines the
shape of the orbital
• Values of l are integers ranging from 0
to n − 1.
• We use alphabetical letters (s, p, d, f) to
communicate the different values of l
and, therefore, the shapes and types of
orbitals (seen in section 6.6)
Magnetic Quantum Number, ml
• Describes the three-dimensional
orientation of the orbital (how the
shape is oriented in space)
• Values 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.
Electronic
Structure
of Atoms
Quantum Numbers
Value of n
1
2
3
4
Value of l
(n-1)
0
1
2
3
d
f
Type of
orbital
Value of ml
(-l  l )
s p
0
(1)
-1, 0,
1
(3)
-2, -1, -3, -2, -1,
0, 1, 2 0, 1, 2, 3
(5)
(7)
• Orbitals with the same principle quantum
number, n, form an electron shell.
• Different orbital types within a shell are
subshells  1s;
2s, 2p;
3s, 3p, 3d;
4s, 4p, 4d, 4f
Table 6.2
Practice:
• What is the designation for the subshell
with…
n = 5 and l = 3? … 5f
n = 3 and l = 2? … 3d
• How many magnetic quantum #s (ml )
are involved in each subshell? Label
them
 n = 5 and l = 3? … 7 = -3, -2, -1, 0 , 1, 2, 3
 n = 3 and l = 2? … 5 = -2, -1, 0 , 1, 2
6.6
Representations of
Orbitals
Electronic
Structure
of Atoms
Orbital Shapes
• Recall…the shape of an orbital is described
by its azimuthal quantum #, l
• l=0=s
 every n value has an l of 0, thus an s orbital
• l=1=p
 only n = 2 or above has an l of 1, thus a p orbital
• l=2=d
 only n = 3 or above has an l of 2, thus a d orbital
• l=3=f
 only n = 4 or above has an l of 3, thus a f orbital
Electronic
Structure
of Atoms
s Orbitals
• Lowest energy orbitals
• Spherical in shape
• Radius of sphere
increases with
increasing value of n
Electronic
Structure
of Atoms
s Orbitals
Graph - 6.18:
Probability of finding
an e– Vs. distance
from the nucleus…
 s orbitals possess
nodes, which are
regions where there is
zero probability of
finding an e–
 The likelihood of
finding e– further from
then nucleus
increases as the n
value increases
Electronic
Structure
of Atoms
p Orbitals
• “dumbbell” shaped
 e– density concentrated on either side of the nucleus
(two lobes with a node between them)
• Since there are 3 ml values for p orbitals, there
are 3 orientations in space (px, py, pz)
 For the same n value, each orientation is the same size
& of equal energy (larger n = bigger & more energy)
Electronic
Structure
of Atoms
d Orbitals
• There are five d
orbital orientations
 4 of them have 4
lobes like “four-leaf
clovers”
 the 5th resembles a
p orbital with a
doughnut around
the center.
 For a given n, all 5
orientations have
equal energy
(orbitals w/same
energy are known
as degenerate)
Electronic
Structure
of Atoms
f Orbitals
• There are seven f orbital orientations
 For a given n, all 7 orientations are degenerate
(have equal energy)
Electronic
Structure
of Atoms
6.7
Many-Electron
Atoms
Electronic
Structure
of Atoms
Energies of Orbitals
• In a hydrogen atom, (where there is only one e–)
all the orbitals with the same n value have the
same amount of energy regardless of orbital
shape (s, p, d, & f are degenerate)
Energies of Orbitals
• For multi-electron atoms, as the # of e–
increases, so does the repulsion between them.
• Therefore, in multi-electron atoms, orbitals of the
same n energy level are NOT degenerate.
Energy
Level
Diagram
• The energy of
the orbital
increases as the
l value increases
 Energy for a
given n value is,
s<p<d<f
* notice, all five 3d
orbitals are still
degenerate (same
energy level) but
3s < 3p < 3d
Electronic
Structure
of Atoms
The 4th Quantum Number:
Spin Magnetic Quantum Number, ms
• In the 1920s, it was
discovered that 2 e– in the
same orbital, say a 2s, do not
have exactly the same
energy.
• The “spin” of an e– describes
the direction it spins in a
magnetic field, which affects
its energy.
This lead to 4th quantum #
• The spin quantum number
has only 2 values:
+1/2 and −1/2
Electronic
Structure
of Atoms
Pauli Exclusion Principle
• NO two e– in the same
atom can have the same
set of all 4 quantum
numbers  n, l, ml , ms
 Each orbital may hold a
maximum of 2 e–, provided
they have opposite spins (ms
values)
Ex) A 3px orbital has the
same n, l, ml values but one
e– must be +1/2 & one -1/2 to
exist in the same orbital
Electronic
Structure
of Atoms
Orbitals & Electrons in Sublevels
Sublevel
s
p
d
f
# Orbitals
1
3
5
7
Max #
electrons
2
6
10
14
* Each orbital can hold a max. of 2 e–
6.8 - 6.9
Electron
Configurations
Electronic
Structure
of Atoms
Three rules are used to build the
electron configuration:
Pauli Exclusion Principle
Aufbau principle
Hund’s Rule
Electronic
Structure
of Atoms
Pauli Exclusion Principle
• An orbital can hold only a max. of two
electrons and they must have opposite
spins.
• Electron Spin:
+1/2 or -1/2
Electronic
Structure
of Atoms
Aufbau Principle
• Electrons occupy orbitals of lowest
energy first.
Generally, as n increases, the
energy increases and s < p < d < f
However, this is not always the
case…
Increasing energy
7s
7p
6p
6s
5s
5p
4p
4s
3p
3s
2s
1s
2p
6d
5d
4d
3d
5f
4f
Diagram:
Orbital
Filling
Electronic
Structure
of Atoms
Blocks in the Periodic Table
Electronic
Structure
of Atoms
Hund’s Rule
• For degenerate orbitals (ex: the three p, five
d, or seven f orbitals), the most stable atom
(lowest energy) is attained when the
number of e– with the same spin is
maximized
• e– fill orbitals with parallel spins before
paring up
Analogy: Students fill each seat of a school bus, one
person at a time, before sitting together.
Types of Electron Configurations
• Orbital Diagrams
shows electrons filling the sublevels in order
each box represents one orbital sublevel
uses arrows to represent e–
direction of the arrow represents the spin of
the electron.
• Standard Electron Configuration
• Condensed Electron Configuration
uses the noble gases as a shortcut
Electronic
Structure
of Atoms
WS
Packet
pg. 1
Orbital
Diagram for
Hydrogen
# e– = 1
Aufbau
Principal!
Orbital
Diagram for
Helium
# e– = 2
Pauli Exclusion
Principal!
Electronic
Structure
of Atoms
Orbital
Diagram for
Lithium
# e– = 3
Electronic
Structure
of Atoms
Orbital
Diagram for
Beryllium
# e– = 4
Electronic
Structure
of Atoms
Orbital
Diagram for
Boron
# e– = 5
Electronic
Structure
of Atoms
Orbital
Diagram for
Carbon
# e– = 6
Hunds Rule!
Electronic
Structure
of Atoms
Orbital
Diagram for
Nitrogen
# e– = 7
Electronic
Structure
of Atoms
Orbital
Diagram for
Oxygen
# e– = 8
Electronic
Structure
of Atoms
Electron Configurations
• Distribution of all
e– in an atom
• Consist of…
Number denoting
the principle
energy level, n
(also called an e–
shell)
Electronic
Structure
of Atoms
Electron Configurations
• Consist of …
Letter denoting
the type of orbital
(subshell)
Electronic
Structure
of Atoms
Electron Configurations
• Consist of…
Superscript
denoting the
number of
electrons in that
orbital/subshell.
Electronic
Structure
of Atoms
Standard Electron Configurations
• Oxygen, 8 e–
1s22s22p4
• Neon, 10 e–
1s22s22p6
 notice that the 2nd energy level (shell) is
completely full  2 s and 6 p = 8 e– (octet)
 outer most energy level being full makes
noble gases very stable
Electronic
Structure
of Atoms
Condensed (Noble Gas) E.C.
• Use the LAST noble gas that is located in the
periodic table right before the element.
• Write the symbol of the noble gas in brackets.
• Write the remaining configuration after the
brackets.
Aluminum:
1s22s22p63s23p1
or
[Ne] 3s23p1
• The noble gas represents the inner “core” e–
• The remaining configuration focuses on the
valence e– in the outermost shell (energy level)
Valence Electron Trend
- down a column -
Electronic
Structure
of Atoms
Some Anomalies
• Some irregularities occur when there are enough
e– to half-fill s and d orbitals on a given row.
• Ex) Chromium:
we would expect: [Ar] 4s2 3d4.
but really the E.C. is: [Ar] 4s1 3d5
• Because the 4s and 3d orbitals are very close in
energy, an e– is moved from the s to the d orbital
so that both are HALF-FULL
• Molybdenum and Tugsten behave the
Electronic
same way
Structure
of Atoms
Some Anomalies
• A similar instance occurs with copper
• Ex) Copper:
we would expect: [Ar] 4s2 3d 9.
but really the E.C. is: [Ar] 4s1 3d10
• Because the 4s and 3d orbitals are very close in
energy, an e– is moved from the s to the d orbital
so that the s is HALF-FULL and the d is
COMPLETELY FULL
• Silver and Gold behave the same way
Electronic
Structure
of Atoms