CHAPTER 6
The Structure of
Atoms
Chapter Outline
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6-1 Electromagnetic Radiation
6-2 Quantization: Planck, Einstein, Energy and
Photons
6-3 Atomic Line Spectra and Niels Bohr
6-4 Particle-Wave Duality: Prelude to Quantum
Mechanics
6-5 The Modern View of Electronic Structure: Wave
or Quantum Mechanics
6-6 The Shapes of Orbitals
6-7 One More Electron Property: Electron Spin
Atomic Structure
A model describing the structure of an atom.
When Atoms react It is the ELECTRONS that react
Much of our understanding of ELECTRONS comes
from Analysis of the Absorption or Emission of Light
Electromagnetic Radiation
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Atoms gain energy and they become
excited
Added energy is absorbed by electrons
and then released in the form of
“Electromagnetic Radiation”
Outer atom is almost vacuum
Electromagnetic Radiation
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energy traveling through space
particles or waves? More on this later
c = 
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c = speed of light 2.998 × 108 ms−1
 = wavelength lambda typically nm
 = frequency nu s−1 or a hertz
Electromagnetic Radiation
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Consists of oscillating electric and
magnetic fields traveling through space
Travel at the same rate-----speed of
light in a vacuum
Typical units
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c = 3.00  108 m/s
c = 3.00 108 ms−1
 = s−1 or cycle/s or Hertz (Hz)
 = distance
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radio waves - m
visible light - nm (10−9 m)
Electromagnetic Radiation
Electromagnetic Radiation or “Light” is
composed of two orthogonal vectors:
An electric wave and a magnetic wave.
Electromagnetic Radiation
wavelength
Amplitude
wavelength
Node
Ultraviolet radiation
Red is lowest
The intensity of
light is a function
of the wave’s
amplitude.
A point of zero
amplitude is
called a “node”.
Electromagnetic Radiation
Light is characterized by its wavelength and
frequency.
Electromagnetic Radiation
Cell phone’s radiation is between Microwave and Radio waves
Dangerous light is started by UV.
Till rainbow region to long radio waves is safe.
The visible region of the electromagnetic spectrum is only a
small portion of the entire spectrum.
Niels Bohr/Max Planck Discovered
Quanta
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If you were told that you could drive
your car at 23.4 mph or 28.9 mph or
34.2 mph, but never any speed between
in between these values…..you wouldn’t
believe it!!
Yet they discovered this about electrons
in atoms.
What are Quanta?
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In 1900 the German physicist Max
Planck proposed that light, heat, and
other forms of radiation come in tiny
bundles, which he called quanta. The
amount of energy in a single particle, he
said, depended on the frequency and
can be given by the following equation:
E=h where  is the frequency of the
wave and h is a constant that came to
be called Planck's constant.
Quantization of Energy
Max Planck (1858-1947)
proposed that light waves
existed as discrete packets of
energy, “quanta” in order to
account for the prediction that
an ideal black body at thermal
equilibrium will emit radiation
with infinite power. According
to classical physics, the
intensity of emitted light
approaches infinity as the
wavelength of the light
approaches zero.
Quantization
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Packet of energy
Planck (1900); 1918 Nobel Prize
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Energy = hv
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Energy is restricted
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h = 6.63 10−34 J s
E = h, E = 2h, E = 3h, …
Energy is quantized
Since h is small, macroscopic level
energy appears to be continuous.
Quantization of Energy
An object can gain or lose energy by absorbing or
emitting radiant energy in QUANTA. A quanta of
energy is the smallest unit of energy that may be
exchanged between oscillators or emitted as
radiation. It is too small to be observed in the
classical world in which we live.
Energy of radiation is proportional to frequency
Energy = h · v
h = Planck’s constant = 6.6262 × 10−34 J·s
Planck’s Law
E = hν
yields:
E
and
c


hxc

• As the frequency of light increases, the energy of
the photon increases.
• As the wavelength of light increases, the energy
of the photon decreases.
Blue Light, (higher frequency) has more energy than
Red Light, with a lower frequency.
Real World
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Similar to Rungs on a ladder
Or Notes on a piano
Flip books
Photoelectric Effect
Photoelectric Effects
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Certain metals will release (eject) electrons
when light strikes the metal surface.
The energy of the light must exceed a
minimum or “threshold energy” for this to
occur.
Any excess energy beyond this minimum
goes into the kinetic energy of the ejected
electron. (They fly away with greater
velocity).
Photoelectric Effect
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Classical theory suggests that energy of an ejected
electron should increase with an increase in light
intensity.
This however is not experimentally observed!
No ejected electrons were observed until light of a
certain minimum energy is applied.
Number of electrons ejected depends on light
intensity so long as the light is above a minimum
energy. (This “minimum energy” is also the ionization
energy of the metal.)
Photoelectric Effect
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Conclusion: There is a one-to-one
correspondence between ejected electrons
and light waves.
This can only occur if light consists of
individual units called “PHOTONS” .
A Photon is a packet of light of discrete
energy.
The Gist of the Photoelectric Effect
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Demonstrated that light, usually
considered to be a wave, can also have
the properties of particles, albeit
WITHOUT MASS
More on Photoelectric
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For each metal there is a threshold
wavelength On Periodic Table
Cesium
can emit electrons with red
ㄴGroup 1
light, some other metals require yellow
light or even ultraviolet to emit
Intensity vs. Energy
Why not just shine a “bright light?”
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Carnival game analogy - knock down
the bottles
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which would you choose?
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A
B
50 nerf balls
1 baseball
50 nerf balls - more intense
1 baseball - more energy
Photoelectric Effect
Evidence for Quanta
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Einstein (1905); 1921 Nobel Prize
Video game analogy
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nickels and dimes, no matter how many,
will not get a video game to work
1 quarter is required
Line Spectra
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Gases are “excited”
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electrons have more energy than normal
as electrons go from higher to lower
energy, light is emitted
Line Emission Spectra of Excited Atoms
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Excited atoms emit light of only certain
wavelengths.
The wavelengths of emitted light are
unique to each individual element.
Atomic Spectra and Bohr
One view of atomic structure in early 20th century was
that an electron (e-) traveled about the nucleus in an orbit.
1. Any orbit should be possible and so is any energy.
2. But a charged particle moving in an electric field
should emit energy.
End result should be destruction!
Atomic Spectra and Bohr Model
Bohr asserted that line spectra of elements indicated
that the electrons were confined to specific energy
states called orbits.
The orbits or energy levels
are “quantized” such that
only certain levels are
allowed.
+
n = 1, 2, 3... 
The Bohr Model:
r n = n 2ao
ao = Bohr radius (53 pm)
Atomic Spectra and Bohr Model
Bohr asserted that line spectra of elements indicated
that the electrons were confined to specific energy
states called orbits.
+
The lines (colors)
corresponded to “jumps” or
transitions between the
levels.
Atomic Spectra and Bohr
Bohr said classical view is wrong.
Need a new theory — now called QUANTUM
or WAVE MECHANICS.
e- can only exist in certain discrete orbits —
called stationary states.
e- is restricted to QUANTIZED energy states.
Energy of state = − c/n2
where n = quantum no. = 1, 2, 3, 4, ....
Atomic Line Spectra and Niels Bohr
Line Spectra of H, Hg, and Ne
Line Spectrum of Hydrogen
Balmer series - empirical
30 years before it was explained
Bohr Model
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E is negative (–) for all values of n
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lower (more –) values — more stable
lowest for n = 1 — most stable
zero (0) for n = 
Line Spectrum of Hydrogen
Electron is very stable = 1
Energy Transitions
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ground state - lowest energy level (n=1)
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excited state - higher energy level than
the ground state (n>1)
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E = 0; electron completely separated
from H nucleus (n = )
The Balmer Equation
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Mathematical relationship among observed
frequencies.
An equation was found that could calculate
the wavelength of the red, green, an blue
lines in the visible emission spectrum of
HYDROGEN.
Calculating E
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E = Efinal – Einitial
v equals the wave number not frequency
1
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1 1
   Rh  2  2 
 2 n2 
When n >2
Knowing that R = Rydberg constant =
1.0974 × 107 m−1
Excited State Energy Absorption
Bohr Model - Summary
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Successes - describes the line spectra
of the hydrogen atom
Limitations - only works for 1-electron
systems (H, He+)
Bohr - 1929 Nobel Prize
“If light can be viewed in terms of both wave
and particle properties, why cant particles of
matter, such as electrons, be treated the
same way?”
Yes.
But it’s so small. You cannot see.
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DeBroglie
Matter has wave properties
h

mv
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1 J = 1 kgm2  s−2
h = 6.63 × 10−34 J  s Planck’s constant
m = mass
v = velocity
DeBroglie
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Matter has wave properties
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not observable for big pieces of matter, such as
golf balls
observable for small pieces of matter such as
electrons
Wavelength of a Golf Ball
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82.5 g, v = 255 km/hr (150 mph)
 = 1.13 × 10−34 m
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big particle; very short wavelength
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Wavelength of an Electron
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9.11 × 10−28 g, v = 3.00 × 107 m/s
 = 2.43 × 10−11 m
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small particle, longer wavelength
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Wave or Quantum Mechanics
 Taking on the ideas of Bohr, de Broglie and
Heisenberg, Irwin Schrödinger proposed that matter
can be described as a wave.
 In this theory, the electron is treated as both a wave
and a particle.
 An electron is described by a Wave Function “”
that completely defines a system of matter.
Quantum Mechanics
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e– has only certain allowed energies
results presented
 from mathematical relationship of Schroedinger
(Nobel Prize, 1932)
 wave function  — no physical meaning
 2 — probability of finding an electron in a region
in space (orbital)
Always ends at 0
Wave motion: wave length and nodes
“Quantization” in a standing wave
From the book in search of
Shrodinger’s cat
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If it were ever possible to know the
position and velocity of every particle in
the universe, then it would be possible
to predict with utter precision the future
of every particle and therefore the future
of the universe.
Uncertainty principle
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Heisenberg (1932 Nobel Prize)
for an electron, cannot know
simultaneously both
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position
momentum
observation affects behavior
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mouse - flashlight analogy
stick in stream analogy
Types of Orbitals
• The solutions to the
Schrödinger equation
yields the probability in
3-dimensons for the
likelihood of finding an
electron about the
nucleus.
• It is these probability
functions that give rise to
the familiar hydrogen-like
orbitals that electrons
occupy.
Every orbital’s maximum electron is 2
Quantum Numbers & Electron Orbitals
Quantum Numbers are terms that arise from the mathematics
of the Schrödinger equation. They describe location of an
electron in a particular orbital much like an address.
Each electron in an orbital has its own set of three quantum
numbers.
“n”= 1, 2, 3, 4…up to infinity
Principal Quantum Number
shell
Azimuthal or Angular Quantum Number
“l” = 0, 1, 2, 3…up to a maximum of “n – 1”
sub-shell
Magnetic Quantum Number
“ml” ml may take on the value an integer from – l to + l
individual orbitals
Quantum Numbers & Electron Orbitals
n defines the Principal energy level “shell”
There are n “sub–shells” for each n – 1 level corresponding to l
if “n” equals:
n=1
n=2
n=3
“l” can have values of:
l=0
l=0&1
l = 0, 1 & 2
Each l is divided into (2l + 1) ml “orbitals” separated by
orientation.
if “l” equals: “ml” can have values of:
l=0
ml = 0
l=1
ml = 0, ±1
l=2
ml = 0, ±1, ±2
Quantum Numbers & Electron Orbitals
Each “l” within an “n-level” represents a sub-shell.
Each “l” sub-shell is divided into ml degenerate
orbitals, where ml designates the spatial orientation
of each orbital.
l=0
l=1
l=2
l=3
Type of orbital
“s” sub-shell (sharp)
“p” sub-shell (Principal)
“d” sub-shell (diffuse)
“f” sub-shell (fine)
# of orbitals
1
3
5
7
each subshell contains 2l+1 orbitals
Orbitals
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The region in which an electron can be
found within an atom
Orbitals and Quantum Numbers
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Orbitals have a characteristic size and
shape
n = principal QN; energy and size
 l = angular momentum or azimuthal QN;
shape
 ml = magnetic QN; orientation
orbitals with same n in same shell
orbitals with same n & l in same subshell
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QN Summary:
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n, l, ml describe an orbital
ms describes spin of e– in an orbital
a set of 4 QN describes an e–
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like an address describes a location
no two e– in an atom can have identical
sets of 4 QN’s
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Pauli Exclusion Principle
Summary of Quantum Numbers
Allowed Quantum Numbers
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n = 1,2,3, ….
l = 0,1,2, ….(n-1)
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l = 0, s
l = 1, p
l = 2, d
l = 3, f
ml = (-l …., 0, …. +l)
Types of Orbitals
s orbital
p orbital
d orbital
s-Orbitals
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l = 0, ml = 0
2l+1 = 1
one s-orbital that extends in a radial manner from
the nucleus forming a spherical shape.
p-Orbitals
The three degenerate p-orbitals spread out on the x, y
& z axis, 90° apart in space.
d-Orbitals
s-orbitals have no nodal
planes (l = 0)
p-orbitals have one
nodal plane (l = 1)
d-orbitals therefore have
two nodal planes (l = 2)
Arrangement of Electrons in Atoms
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Each orbital can accommodate no more than 2
electrons
Since each electron is unique, we need a way
to distinguish the individual electrons in an
orbital from one another.
This is done via the 4th quantum number, “ms”.
Stern-Gerlach Experiment (1922)
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If atoms with a single unpaired electron are
placed in a magnetic field, they showed there
are two orientations for the atoms.
The electron spin was aligned with the field or
opposed to the field.
Electron Spin
Since there were 2 pathways in the Stern-Gerlach
experiment, there must be 2 spins affected by the
magnetic field. One spinning to the right, one spinning
to the left.
Each “spin state” is assigned a quantum number
ms = ± ½
+ ½ for “spin up”
 ½ for “spin down”
Electron Spin
Electron Spin
Quantum
Number, ms
The experiment results indicate that electron has an
intrinsic property referred to as “spin.”
Two spin directions are given by
ms where ms = +1/2 and -1/2.
Electron Spin
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It is not that the electrons are actually spinning
on axis...
Rather it is that the mathematics that describe
the electrons “looks” like they are spinning on
axis.
ms, e– spin
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ms, spin quantum number, indicates
spin
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ms = +½
ms = –½
Magnetic Properties of Atoms and Ions
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Paired electrons – diamagnetic
Ferromagnetic- metals with magnetic
properties
Unpaired electrons - paramagnetic
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attracted by a magnetic field
attraction proportional to number of unpaired e–
Electron Spin and Magnetism
• Diamagnetic Substances: Are NOT attracted to
a magnetic field
• Paramagnetic Substances: ARE attracted to a
magnetic field.
• Substances with unpaired electrons are
paramagnetic.