Quantum Theory and the
Electronic Structure of
Atoms
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Once scientists developed a logical order for
the elements they began studying the
structure and composition of individual
atoms.
They used substances’ interactions with light
to explain the structure of atoms and develop
a model to explain how atoms affected
properties of light.
In order to understand interactions, we must
understand behavior of light.
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Light is typically described as traveling in waves
(similar to water); All electromagnetic (EM)
waves (including light) are made of two
components: electric and magnetic
EM waves travel at the speed of light, c
(2.997924 x 108 m/s ≈ 3.00 x 108 m/s)
c = ln (Know these variables!)
c = speed of light;
l (lambda) = wavelength (m, nm);
n (nu) = frequency (1/s, s-1, Hz)
EM waves
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Different colors of light correspond to
different wavelengths in the visible portion of
the EM spectrum. Two wavelengths (l) are
shown below. Determine the frequency (n)
for each wave.
Blue light
Red light
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1 nm = 1 x 10-9 m OR
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1 x 109 nm = 1 m
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Classical descriptions:
◦ Dalton: atoms are hard particles, all atoms of the
same element are the same
◦ Thomson: atoms are divisible (electrons in atoms)
◦ Rutherford: positively charged nucleus
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New view of atomic behavior
◦ Planck: Blackbody radiation – heat solids to red or
white heat, matter did not emit energy
continuously; in whole-number multiples of certain
quantities
◦ Matter absorbs or emits energies in packets quanta
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Quantum has come to mean small; originated
from Planck’s observation of quantized
energy
Einstein used this theory to observe metals
reacting to different colors of light –
Photoelectric Effect: electrons are ejected
from the surface of certain metals exposed to
light at a certain minimum frequency
◦ Blue light (n = 6.7 x 1014 Hz) causes Na to emit
electrons, red light (n = 4.0 x 1014 Hz) does not
Photoelectric Effect
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Based on photoelectric effect, light acts as a
wave but also exists as a stream of particles
called photons
Energy of photons is proportional to
frequency, inversely proportional to
wavelength
hc
E  hn 
-34 J•s
h
=
6.626
x
10
l
J = kg • m2 / s2
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1) Which has a higher frequency: light from a red
stoplight with a wavelength of 750 nm or a yellow
light with a wavelength of 600 nm?
2) What is the wavelength of a radio station’s waves
transmitting at a frequency of 101.5 MHz
(megahertz)? (FM radio waves range from 30 – 300
MHz.)
3) Red lights at traffic stops have wavelengths of
about 650 nm. What is the frequency (in Hz) of
this light?
4) Calculate the energy (in Joules) of a photon with
a wavelength of 5.00 x 104 nm (infrared region).
Answers: yellow, 2.956 m, 4.62 x 1014 Hz, 3.98 x
10-21 J
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de Broglie: If light can behave like a wave and
a particle, then matter (i.e., electrons) can
behave like a wave
If an electron behaves like a standing wave,
then it can only have specific wavelengths
Can calculate wavelength for matter if we
know its velocity (use v instead of c):
l = h / m v (This is the de Broglie equation.)
◦ h = Planck’s constant, m = mass (electron’s have
constant mass: 9.11x10-31 kg), v = velocity (speed)
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The energy of a photon is 5.87 x 10-20 J.
What is the frequency of the photon?
What is the wavelength of an electron that
travels at 34.7 m/s and has a mass of 9.11 x
10-31 kg?
A 0.143 kg baseball is thrown at a velocity of
42.5 m/s. Calculate the wavelength of the
baseball. How does the baseball’s
wavelength compare to the electron from the
example above?
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Calculate the energy of a photon that has a
wavelength of 35.6 nm (in the x-ray region).
(Hint: Watch units!!!)
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If electrons have wavelike properties, then we
can’t know both its position and velocity. In
order to determine the position of an
electron, we hit it with a photon of light, but
this will change its position and velocity.
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Bohr sought to reconcile these views of the
electron.
◦ Developed the planetary analogy of atoms.
◦ Electrons orbit around the nucleus like planets
around the sun.
◦ Electrons travel in discrete, quantized circular
orbits; like going up or down stairs.
◦ Each orbit has a specific energy associated with it,
labeled as n = 1, 2, etc.
◦ Ground state is the lowest energy level for an atom
(n = 1).
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When an atom absorbs energy, an electron
can jump from a lower energy level to a
higher energy level.
When an atom emits (releases) energy, an
electron drops from a higher energy level to a
lower energy level. This process sometimes
gives off energy as visible light.
H e- transitions
Eng. Color
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White light we see consists of all colors in
the visible spectrum. Use a prism (or CD) to
break them up.
cont. spect.
white light
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Light given off by atoms
doesn’t necessarily correspond to all visible colors.
Flame tests
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Hydrogen
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Each element gives
off unique spectrum
Demo: Gas Discharge
Tubes
◦ Each element has its
own individual emission
spectrum. This allowed
scientists to identify
elements in different
minerals.
Spectra of Elements:
http://www.wwnorton.com/college/chemistry/chemconnections/BlueLight/pages/elements.html
Figure 7.8
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The Bohr model worked well for hydrogen,
but failed for elements with more than one
proton and one electron.
Quantum Mechanics was developed (by
Schrödinger in the 1920’s) to describe the
motion of subatomic particles
◦ Did not attempt to describe position of particles;
used mathematical equations to describe the
probability of finding the particles
◦ The probability density (map of likely locations) is
the “electron cloud”
Quantum Mechanics Movie
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The region of highest probability for finding
an electron is an “electron cloud”. This
region of high probability is called an atomic
orbital. Each orbital holds at most 2
electrons.
Modern atom.exe
e- orbit vs
e- cloud
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There are 4 quantum number that describe
the size, shape, and location of electrons
We use these numbers to describe where
electrons are found for an atom. Can also
use the periodic table!!!
The Principal Quantum Number, n
◦ describes distance of the electron from the
nucleus; called shells
◦ n = 1, 2, 3, etc; larger number is farther from
nucleus
◦ n corresponds to a row in the periodic table
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The Angular Momentum Quantum Number, l
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The Magnetic Quantum Number, ml
◦ describes the orientation of the orbital with respect to x, y,
◦ In each row of the periodic table are different groups of
orbitals with different shapes. These groups of orbitals are
called subshells and labeled s, p, d, and f.
◦ s subshells are spherical (first two columns)
◦ p subshells are dumb-bell shaped (last six columns)
◦ d subshells are intersecting dumb-bells (transition metals)
and z axes
◦ s, p, and d orbitals have different shapes and therefore
different orientations
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The Spin Quantum Number, ms
◦ describes the spin of an electron in an orbital (shown as up
and down arrows in orbital diagrams)
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s orbitals are
spherical; white
rings are nodes
(regions where an
electron won’t be
found)
◦ 1 s orbital in a
subshell
s orbital
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2px orbital
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2py orbital
2pz orbital
p orbitals are dumb-bells (2 lobes); node
between lobes
◦ 3 p orbitals in a subshell
p orbital
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d orbitals: intersecting dumb-bells (4
lobes); nodes between lobes
◦ 5 d orbitals in a subshell
d orbital
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The first shell (row) has 1 subshell (s)
◦ s  only 1 orbital
◦ An s subshell can hold at most 2 electrons
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The 2nd shell (row) has 2 subshells (s and p)
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The 3rd shell (row) has 3 subshells (s, p, and d)
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The 4th shell (row) has 4 subshells (s, p, d, and f)
◦ p  set of 3 orbitals
◦ A p subshell can hold at most 6 electrons
◦ d  set of 5 orbitals
◦ A d subshell can hold at most ? electrons
◦ f  set of 7 orbitals
◦ What is the maximum number of electrons allowed in the f
subshell?
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Arrangement of subshells in the Periodic
Table
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What is the maximum number of:
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electrons allowed in the 2px orbital?
subshells allowed in the 4th shell?
electrons allowed in the 3d subshell?
electrons allowed in the 4d subshell?
electrons allowed in the 3p subshell?
electrons allowed in the 3rd shell?
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In hydrogen, all
shells are equivalent
in energy.
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In many-electron
models, the energy
levels depend on the
shell and subshell.
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Aufbau principle: start with the nucleus and
empty orbitals, then “build” up the electron
configuration using orbitals of increasing
energy.
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Arrangement of subshells in the Periodic
Table
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Arrangement of subshells in the Periodic
Table
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Arrangement of subshells in the Periodic
Table
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Arrangement of subshells in the Periodic
Table
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Arrangement of subshells in the Periodic
Table
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Write electron
configurations for the
following atoms.
H
He
Li
Be
B
N
O
Ne
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Na
Al
S
Ar
K
Sc
Ti
Zn
Br
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Electrons in the outermost shell.
◦ 1s2 2s2 2p6
◦ 1s2 2s2 2p6 3s2 3p5
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Identify the valence electrons (v. e.) in the
following configurations:
◦ 1s2 2s2 2p6 3s2
◦ 1s2 2s2 2p33s2
1s2 2s2
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Rather than writing out complete electron
configurations, we can use the previously
filled shell (noble gas) and show the valence
electrons (v. e.):
P: 1s2 2s2 2p6 3s2 3p3  [Ne] 3s2 3p3 (5 v. e.)
Write the shorthand notation for:
◦
◦
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Ca
Cl
Sr
Fe
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Some exceptions to the Aufbau order…
What are the expected electron
configurations for Cr and Cu?
Filled and half-filled d subshells seem to be
especially stable.
Cr: 1s2 2s2 2p6 3s2 3p6 4s1 3d5
◦ Also true for Mo and W
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Cu: 1s2 2s2 2p6 3s2 3p6 4s1 3d10
◦ Also true for Ag and Au
e_config.
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If two or more orbitals (i.e., a p or d orbital)
with the same energy are available, one
electron goes into each orbital until they have
to pair up.
◦ Fighting sibling analogy
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For example, an atom with 2 p electrons: 1
electron will go into the first (px) orbital, the
next electron will go into the second (py)
orbital.
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Pauli Exclusion Principle: no two electrons
can have the same values of all 4 quantum
numbers
Describes what happens when electrons share
an orbital.
◦ Only two electrons can occupy a single orbital and
they must have opposite spin (i.e., the 4th quantum
number). The first electron is designated as
positive spin (up arrow), the second electron in that
orbital has negative spin (down arrow).
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Orbital
diagrams are
pictorial
representations
of electron
configurations.
Electron Configurations
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Write electron configurations for the
following elements (long-hand notation).
Indicate the number of v.e. for each element.
potassium
sulfur
carbon
magnesium
lithium