Electronic Structure
of Atoms
Dalton’s Atomic Model
• In 1804 Dalton’s Postulates
described the existence of
small indivisible particles
called atoms that make up
all matter.
• There are no electrons,
protons, or neutrons in his
atomic model.
Thomson’s Cathode Ray Tube
• J. J. Thomson experimented with cathode ray tubes.
• Glass tubes are partially filled with gas.
• A high voltage produces a cathode ray in the tube
(originates from negative cathode).
• Cathode rays cause certain materials to fluoresce.
1897 Cathode Ray Tube
Experiment
• Rays are deflected by electric or magnetic fields.
• Ray travels in straight line in absence of electric or
magnetic fields.
• Ray bends away from negative plate, towards
positive plate.
• Metal plate exposed to rays gets a negative charge.
• Ray behavior stays the same regardless of cathode
material.
• What did Thomson conclude from his
experiment?
Thomson’s Conclusion
• Cathode rays are streams of
negatively charged particles with
mass.
• Discovery of the electron!
• The ratio of an electron’s charge
to mass is 1.76 x 108C/g.
• Thomson describes his Plum
Pudding atomic model.
Millikan’s 1909 Oil Drop
Experiment
• Millikan found
the charge on
an electron.
• Then using
Thomson’s
charge-to-mass
ratio, he found
the electron
mass to be 9 .1
x 10-28g.
Radioactivity
• Radioactivity: spontaneous emission of
high-energy radiation. (Henri Becquerel,
Pierre & Marie Curie, Ernest Rutherford)
• Three types of radiation:
• Alpha () rays: particles with 2+ charge
• Beta () rays: particles with 1- charge
• Gamma () rays: no particles, no charge,
high-energy radiation similar to X-rays.
Rutherford’s 1910 Gold Foil
Experiment
• Disproved Thomson’s Plum
Pudding model.
• Passed a beam of alpha
particles through a piece of
gold foil to a fluorescent
screen.
• Most alpha particles passed
directly through foil.
• A few particles deflected at
large angles.
Rutherford’s Conclusions
• Most of the atom
must be empty space.
• There must be a small,
dense region of
positive charge.
• Rutherford discovered
the nucleus!
Rutherford’s New Atomic Model
• Rutherford discovers protons in 1919.
• New atomic model disproves Thomson’s model.
• Chadwick discovers neutrons in 1932.
Dalton’s model
Thomson’s Model
Rutherford’s Model
The Wave Nature of Light
• Electromagnetic radiation (radiant energy)
carries energy through space.
• All electromagnetic radiation travels through a
vacuum at 3.00 x 108 m/s (speed of light).
• Wave characteristics of EM radiation are due to
the periodic oscillations of the intensities of
electronic and magnetic forces.
Parts of a Light Wave
• Wavelength (): distance between two wave peaks (m)
• Frequency (): number of wave cycles per unit of time.
Units of Hertz (Hz) or reciprocal seconds (s-1).
• Amplitude: half the distance from the wave peak to the
trough.
What Is The Relationship Between
Wavelength and Frequency?
c = 
Where:
c = speed of light = 3.00 x 108 m/s
 = wavelength (m)
 = frequency (s-1)
Note:  nd  are inversely proportional. As
wavelength gets shorter, the frequency gets higher; as
wavelength gets longer, the frequency gets lower.
Calculations With Wavelength and
Frequency
• What is the wavelength of
radiation with a frequency
of 7.32 x 1019 s-1?
• 4.10 x 10-12 m
• What is the frequency of
radiation having a
wavelength of 754 nm?
• 3.98 x 1014 s-1
Phenomena Showing Interaction Between
EM Radiation and Atoms
• Black-body Radiation: the emission of light from
hot objects (heated metals)
• Photoelectric Effect: the emission of electrons
from metal surfaces on which light shines
• Emission Spectra: the emission of light from
electronically excited gas atoms
Planck and Black-body Radiation
• Max Planck studied black-body radiation to
understand relationship between temperature
and EM radiation.
• He assumed that energy can be emitted or
absorbed by atoms only in discrete “chunks” of
some minimum size.
• Quantum (“fixed amount”) is the smallest
quantity of energy that can be absorbed or
emitted as EM radiation.
Planck’s Equation
E = h
Where:
E = energy of a single quantum (J)
h = Planck’s constant:
(6.626 x 10-34 J-s)
 = frequency (s-1)
Using the Energy Equation
• Calculate the energy of light with a frequency of
6.00ee14 Hz.
• 3.98 x 10-19 J
• Calculate the wavelength of light having an
energy of 2.54 x 10-20 J.
• 7.83 x 10-6 m
Planck’s Quantum Theory
• Energy is always absorbed or emitted in whole
number multiples of hv (hv, 2hv, 3hv, etc.)
• Allowed energies are quantized (restricted to
certain values).
• Energy changes seem continuous in everyday
life because the gain or loss of a single quantum
goes unnoticed in large objects.
• Planck was awarded Nobel Prize in physics for
quantum theory in 1918.
Albert Einstein and the
Photoelectric Effect
Albert Einstein discovered the photoelectric effect
in 1905. For each metal, there is a minimum
frequency of light below which no electrons are
emitted from the metal’s surface.
There is a threshold energy!
Einstein earned the Nobel Prize
in physics for the photoelectric
effect in 1921.
Einstein and Photons
• Radiant energy striking a metal surface
is a stream of tiny energy packets
called photons.
• Photons behave like particles.
• Each photon must have an energy
proportional to the frequency of the
light in which it travels.
Ephoton = h or Ephoton = hc/
Radiant energy is quantized!
How Does Einstein Explain the
Photoelectric Effect?
• When a photon strikes a metal, it may transfer
its energy to an electron.
• An electron needs a certain amount of energy to
hold it in the metal.
• If the photon has enough energy to meet the
electron’s energy requirement, the electron is
emitted from the metal.
• Excess energy is used as kinetic energy for the
electrons.
Radiant Energy and Spectra
• The radiant energy from a laser emits
a single wavelength (monochromatic)
but most common radiation sources
such as light bulbs and stars emit
many different wavelengths.
A spectrum is produced when
polychromatic radiation is separated
into its different wavelengths.
A spectrum producing light of all colors
is called a continuous spectrum.
Line Spectra
• Not all radiation sources produce a
continuous spectrum.
• When gases are placed in a tube
under reduced pressure with high
voltage, different colors of light are
emitted.
• When light from such tubes are passed through a prism,
only lines of a few wavelengths are seen.
• The colored lines are separated by black regions which
correspond to absent wavelengths.
• These spectra are called line spectra.
Hydrogen’s Spectrum
• There are three groups of lines in hydrogen’s simple
spectrum: the Lyman series (UV), the Paschen series
(IR) and the Balmer series (visible).
• Balmer made an equation (Rydberg Equation) to fit the
hydrogen spectrum in the visible range:
1/ = RH [(1/n21) - (1/n22)]
Where
 = spectral wavelength
n = positive integers with n2 > n1
RH (Rydberg constant) = 1.096776 x 107m-1
Bohr’s Atomic Model Based On
Spectral Lines
Here is Bohr’s
model of the
hydrogen atom
with electron
movement
corresponding to
the spectral lines
observed in the
Lyman, Paschen,
and Balmer series.
Bell Work
1) Calculate the energy of a photon with a frequency of
2.72x1013 1/s.
1.80x10-20 J
2) What wavelength of radiation has photons of energy
7.84x10-18 J?
2.53x10-8 m
In what portion of the electron magnetic spectrum would this
radiation be found?
UV
Niels Bohr’s Atomic Model
• Bohr based his atomic model on
the hydrogen atom with only one
electron.
• He assumed that the electron
moves in a circular orbit around
the nucleus.
• According to classical physics, the
electron should lose energy as it
orbits and spiral into the nucleus.
• Since the electron does not spiral into the nucleus, the old
laws of physics are inadequate to describe the atom.
Niels Bohr’s Atomic Model
Bohr’s Three Postulates
1.
2.
3.
Only orbits of certain radii with certain definite
energies are permitted for electrons in an atom.
An electron in a permitted orbit has a specific energy
and is in an “allowed” energy state. It will not radiate
energy and spiral into the nucleus.
Energy is only emitted or absorbed by an electron as
it changes from one energy state to another. Energy is
emitted or absorbed as a photon (E = h).
Bohr’s Three Postulates
A
B
Energy States of the
Hydrogen Atom
•
•
•
•
•
Bohr equation: E = (-2.18 x 10-18 J) (1/n2)
Integer n (values 1 to ) is called the quantum number.
Each n value corresponds to a different orbit.
The radius of the orbit gets bigger as n increases.
n = 1 is closest to the nucleus; succeeding n’s get
farther away.
• The spacing between the n levels are uneven; the
greatest spacing occurs between the nucleus and n = 1.
• Successive n levels are scrunched closer together.
• Lowest energy state is the ground state; a higher energy
state is an excited state.
Bohr’s Equation for Hydrogen
Changes in Energy States
E = (-2.18 x 10-18 J) [(1/n2f ) - (1/n2i )]
Where ni and nf are the principal quantum numbers
of the initial and final states of the atom,
respectively.
Note: If E is negative, the atom releases energy.
If E is positive, the atom absorbs energy.
Bohr’s Equation Calculations
E = (-2.18 x 10-18 J) [(1/n2f ) - (1/n2i )]
Calculate the wavelength of radiation detected
when an electron in the hydrogen atom moves
from n = 6 to n = 2. 4.10x10-7 m
Is this wavelength visible? Yes
Does the atom release or absorb energy for
this move? Why? Release
Bohr’s Equation Calculations
E = (-2.18 x 10-18 J) [(1/n2f ) - (1/n2i )]
Calculate the change in energy as an
electron moves from n=3 to n=1 level.
ΔE = -1.94x10-18 J
What is it’s wavelength? 1.03x10-7 m
Can we see this wavelength? No
Significance of Bohr Model
• Bohr’s model works best for hydrogen
atom; it does not work well with mutlielectron atoms.
• Bohr’s model treats the electron as
merely a small particle but it also has
wave properties.
• Bohr’s model introduces distinct energy
levels described by quantum numbers.
• Bohr’s model says that energy is needed to move an electron
from one level to another.
• Bohr wins Nobel Prize in physics in 1922.
Is Radiation a Particle or a Wave?
• Depending on experiment, radiation has either
wavelike or particle-like (photon) character.
• Given that wavelengths of radiation have particle-like
character, can matter (made up of particles) have
wavelike character?
Wave-Particle Duality
• Louis de Broglie theorizes that an electron
in its movement about the nucleus does
have a wavelength associated with it.
• De Broglie wins 1929
Nobel Prize in physics for
wave-particle duality.
De Broglie Equation
 = h/mv
Where:
mv = momentum
m = mass (kg)
v = velocity (m/s)
h = Planck’s constant = 6.626 x 10-34 kg m2/s
*Remember that 1 Joule = 1 kg m2/s2
De Broglie Equation Practice
What is the wavelength of an electron
having a mass of 9.11 x 10-28 g and a
velocity of 5.97 x 106 m/s?
1.22x10-16 m
De Broglie Equation Practice
What is the mass of an electron having a
wavelength of 3.10x10-6 m and a velocity
of 7.01x107 m/s?
m = 3.05x10-36 kg
Classical Physics and the Electron
• Using classical physics, we can easily calculate
the position and speed of a ball rolling down a
ramp at any point.
• Classical physics cannot adequately describe the
location of an electron with wave properties.
• Physicist Werner Heisenberg concluded that the
dual nature of matter puts a limitation on how
precisely we can know both the location and
momentum of matter with a very small mass.
Heisenberg’s Equation
Heisenberg makes an equation relating the
uncertainty of an electron’s position (x) and
the uncertainty in its momentum (mv) to
Planck’s constant:
x  mv ≥ ( h/4 )
This equation essentially tells us that if the
mass of an electron is known, its position will
be unknown.
Heisenberg’s Uncertainty Principle
It is impossible to know simultaneously both the
exact momentum of an electron and its exact
location.
Heisenberg’s Uncertainty Principle leads to a new
atomic model in which the energy of an electron is
known but its location is described in terms of
mathematical probabilities.
Heisenberg receives the Nobel Prize in physics for
his uncertainty principle in 1932.
Heisenberg’s Uncertainty Principle
Heisenberg is out for a drive when he's
stopped by a traffic cop.
The cop says, "Do you know how fast
you were going?“
Heisenberg says, "No, but I know
where I am."
Bell Work
E = (-2.18 x 10-18 J) [(1/n2f ) - (1/n2i )]
1. Calculate the wavelength of radiation detected
when an electron in the hydrogen atom moves
from n = 3 to n = 6.
2. Does the atom release or absorb energy for
this move? Why?
3. Describe the Duality Principle.
4. Describe Heisenberg's Uncertainty Principle.
Quantum (Wave) Mechanics
• Erwin Schrödinger uses an equation to
incorporate the wavelike and particle-like
qualities of electrons.
• This became the basis for the quantum
mechanical (wave mechanical) model.
• Schrödinger incorporates series of mathematical
functions (wave functions) that describe the
electron’s matter wave.
• Schrödinger’s work deals with probabilities.
Quantum (Wave) Mechanics
The electron cloud of an atom can be
compared to….
Wave Functions
• Wave functions () describe a matter wave.
• Probability density (2) represents the probability that
an electron will be found at a given location.
• 2= 0 denotes a location where there is no probability
of finding an electron.
• Electron density is a region where there is a high
probability of finding an electron 90% of the time.
• Wave functions are called orbitals.
Electron Density and Orbital
Shape
The s-orbitals
•
•
•
•
All s-orbitals are spherical.
As n increases, the s-orbitals get larger.
As n increases, the number of nodes increase.
A node is a region in space where the probability of
finding an electron is zero.
• At a node, 2 = 0
• For an s-orbital, the number of nodes is (n - 1).
Relative Sizes of s-orbitals
Nodes of s-orbitals
p-orbitals
• There are three p-orbitals px, py, and pz.
• The three p-orbitals lie along the x-, yand z- axes of a Cartesian system.
• The orbitals are dumbbell shaped.
• As n increases, the p-orbitals get larger.
• All p-orbitals have a node at the nucleus.
Representations of p-orbitals
How Do s-orbitals and p-orbitals
Fit Together?
Orbital Hotel
Vocab check:
Shell = Level
Subshell = Sublevel
Within a subshell
there are orbitals
d-orbitals and f-orbitals
• There are five d and seven f-orbitals.
• Three of the d-orbitals lie in a plane bisecting
the x-, y- and z-axes.
• Two of the d-orbitals lie in a plane aligned along
the x-, y- and z-axes.
• Four of the d-orbitals have four lobes each
(cloverleaf).
• One d-orbital has two lobes and a collar
(“double baby binky”).
f-orbitals
Orbitals and Quantum Numbers
• Any electron has a series of 4 quantum numbers:
1. Principal Quantum Number (n). Same as Bohr’s
n. Designates particular energy level and controls size
of orbital. The higher the number for n, the higher
the associated energy. Uses n = 1, 2, 3, …
2. Orbital Angular Momentum Quantum Number
(Azimuthal Quantum Number) (l). Controls
shape of orbital. Depends on the value of n.
Uses l = 0 (s-orbital); l = 1 (p-orbital); l = 2 (dorbital); l = 3 (f-orbital).
Orbitals and Quantum Numbers
Continued
3. Magnetic Quantum Number (ml).
Designates a specific orbital, gives 3D
orientation of each orbital. Has integral
values between -l and +l. For instance, if
l = 2, ml can be -2, -1, 0, 1, or 2.
4. Spin Magnetic Quantum Number (ms).
Indicates spin of electron in the orbital.
Uses ± 1/2.
Orbitals and Quantum Numbers
Orbitals and Their Energies
• In a many-electron atom, the energy
increases in this order: s< p < d < f
• The exact spacing of energy levels and
energy differ from one atom to another.
• All orbitals of a given subshell have the
same energy and are called degenerate.
Bell Work
1. All orbitals of a given subshell have the same energy
and are called __________.
2. The principle quantum number designates
___________.
3. The azimuthal number designates ___________.
4. The magnetic quantum number designates
___________.
5. The spin magnetic quantum number designates
___________.
Electron Configurations
• Electron configurations tell us which orbitals
are assigned for each electron in an atom.
• There are three rules to guide configurations.
• Pauli Exclusion Principle
• Aufbau Diagram
• Hund’s Rule
Pauli Principle and Electron Spin
• Line spectra of many electron atoms show each
line as a closely spaced pair of lines.
• A beam of atoms was passed through a slit and
into a magnetic field and the atoms were then
detected.
• Two spots were found: one with the electrons
spinning in one direction and one with the
electrons spinning in the opposite direction.
Electron Spin
One electron spins clockwise, the other counterclockwise.
Pauli’s Exclusion Principle
• At most, there can be two electrons in a
given orbital and they must have
opposite spin.
• One spins clockwise, the other counterclockwise.
• In block diagrams, we show this as:
 and 
Aufbau Diagram
• Using an Aufbau Diagram, electrons fill in the following
order from bottom to top (lower energy to higher energy):
•
•
•
•
•
•
•
7s 7p
6s 6p
5s 5p
4s 4p
3s 3p
2s 2p
1s
6d
5d
4d
3d
6f
5f
4f
Aufbau Diagram
1. Write the electron configuration for
nitrogen.
2. Write the electron configuration for iron.
Aufbau Diagram
Energy and
Atomic
Orbitals
Remember, as n increases, energy also
increases. Orbitals of increasing energy
begin to overlap because the space
between the energy levels decreases
with increasing n. Recall that the 4s
orbital fills before the 3d orbital.
Aufbau Diagram
Write the electron configuration for lead.
Hund’s Rule
• Hund’s Rule: For degenerate orbitals, the
lowest energy is obtained when the number
of electrons with the same spin is
maximized.
• Therefore, we fill each degenerate orbital
with a single electron spinning in one
direction before we add each orbital’s
second electron spinning in the opposite
direction.
Hund’s Rule
Practice Hund’s Rule by writing electron
configurations and box diagrams for the
following elements:
1. Nitrogen
2. Sulfur
3. Cobalt
Reading Electron Configurations
from the Periodic Table
Coloring Time!
Condensed Electron
Configurations
• Neon completes the 2p subshell.
• Sodium marks the beginning of a new row.
• So, we write the condensed electron configuration for
sodium as
Na: [Ne] 3s1
• [Ne] represents the electron configuration of neon.
Core and Valence Electrons
• Core electrons: Electrons in closed shells. Usually in the
[brackets] in condensed e- configs.
• Valence electrons: Electrons in the outermost principal
quantum level and unfilled lower quantum numbers of
an atom. (Electrons in d sublevel are often not counted
as valence electrons.) Valence electrons participate in
chemical rxns and are responsible for some physical
properties. Write electron configurations in order of
increasing n to see valence electrons more clearly.
• [Ar]3d84s2 [Core] Valence
• [Ar]3d104s24p1 [Core] Valence
Unusual Electron Configurations
• Elements Ce - Lu have the 4f orbitals filled and
are called lanthanides or rare earth elements.
• Elements Th - Lr have the 5f orbitals filled and
are called actinides. Most actinides are not found
in nature.
• The first three lanthanides and actinides have
unusual electron configurations.
• La: [Xe]6s25d1 Ce: [Xe]6s25d14f1 Pr: [Xe]6s24f3
Anomalous Electron Configurations
• Some common transition elements do not
follow the usual pattern for electron filling.
Element
Actual
Expected
Cr
[Ar]3d54s1
[Ar]3d44s2
Cu
[Ar]3d104s1
[Ar]3d94s2
Ag
[Kr]4d105s1
[Kr]4d95s2
Bell Work
Electronic Structure of Atoms
Hoopla Game
Blue: Cloodle (Without talking or using numbers or letters,
try to get the other players to guess what you’re
drawing.)
Yellow: Tongue-Tied (Use words other than listed on the
slip to get the other players to guess the topic.)
Green: Soundstage (Act out your topic using appropriate
gestures and sound effects.)
Red: Tweener (Use clues like “It’s bigger than ______ but
smaller than ________.” to describe your topic.)
Purple: Wild (Your choice!)