Chapter 7 Quantum Theory and Atomic Structure

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Chapter 7Quantum Theory andAtomic Structure
Read/Study Chapter 7 Suggested Problems
Sample Problems - 7.1 - 7.7 Follow-up Problems
7.1 7.7 Work as many of the
End-of- Chapter problems as you can. Watch
the Videos about The Atom!
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ATOMIC STRUCTURE
Definition of Chemistry
The study of the properties, composition,
and STRUCTURE of matter, the physical and
chemical changes it undergoes, and the
energy liberated or absorbed during those changes.
The foundation for the STRUCTURE of
inorganic materials is found in the STRUCTURE of
the atom.
Material Properties
Bulk Structure
Molecular Structure
Atomic Structure
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ATOMIC STRUCTURE
Historical Development

• Greek Concepts of Matter
• Aristotle - Matter is continuous, infinitely
• divisible, and is composed of only 4 elements
• Earth, Air, Fire, and Water
• Won the philosophical/political battle.
• Dominated Western Thought for Centuries.
• Seemed very logical.
• Was totally WRONG!!

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ATOMIC STRUCTURE
The Atomists (Democritus, Lucippus, Epicurus,
et. al.) - Matter consists ultimately of
indivisible particles called atomos
that canNOT be further subdivided or
simplified. If these atoms had space between
them, nothing was in that space - the void.

• Lost the philosophical/political battle.
• Lost to Western Thought until 1417.
• Incapable of being tested or verified.
• Believed the four elements consisted of
• transmutable atoms.
• Was a far more accurate, though quite imperfect
• picture of reality.

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ATOMIC STRUCTURE
Modern Concepts of Matter
John Dalton (1803) - An atomist who
formalized the idea of the atom into a viable
scientific theory in order to explain a large
amount of empirical data that could not be
explained otherwise.

• Matter is composed of small indivisible
  particles
• called atoms.

• The atoms of each element are identical to each
  
• other in mass but different from the atoms of
  other
• elements.

• A compound contains atoms of two or more
• elements bound together in fixed proportions
• by mass.

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ATOMIC STRUCTURE

• A chemical reaction involves a rearrangement of
• of atoms but atoms are not created nor
  destroyed
• during such reactions.

Present Concepts - An atom is an
electrically neutral entity consisting of
negatively charged electrons (e-) situated
outside of a dense, posi- tively charged nucleus
consisting of positively charged protons (p) and
neutral neutrons (n0).
Particle Charge Mass Electron - 1
9.109 x 10 -28 g Proton 1 1.673 x 10
-24 g Neutron 0 1.675 x 10 -24 g
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ATOMIC STRUCTURE
Nucleus
Model of a Helium-4 (4He) atom
pno
e-
e-
no p
Electron Cloud
How did we get this concept? - This portion of
our program is brought to you by
Democritus, Dalton, Thompson, Planck, Einstein,
Millikan, Rutherford, Bohr, de Broglie,
Heisenberg, Schrödinger, Chadwick, and many
others.
CHRISTMAS
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ATOMIC STRUCTURE
Democritus - First atomic ideas Dalton - 1803 -
First Atomic Theory J. J. Thompson - 1890s -
Measured the charge/mass ratio of the electron
(Cathode Rays)
Fluorescent Material
_
Cathode

Anode
Electric Field Source (Off)
With the electric field off, the cathode ray is
not deflected.
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ATOMIC STRUCTURE
-
Fluorescent Material
-
Cathode


Anode
Electric Field Source (On)
With the electric field on, the cathode ray is
deflected away from the negative plate. The
stronger the electric field, the greater the
amount of deflection.
-
Cathode

Anode
Magnet
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ATOMIC STRUCTURE
With the magnetic field present, the cathode ray
is deflected out of the magnetic field. The
stronger the magnetic field, the greater the
amount of deflection.
e/m E/H2r
e the charge on the electron m the mass of
the electron E the electric field strength H
the magnetic field strength r the radius of
curvature of the electron beam
Thompson, thus, measured the charge/mass ratio of
the electron - 1.759 x 108 C/g
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ATOMIC STRUCTURE

• Summary of Thompsons Findings
• Cathode rays had the same properties no matter
• what metal was being used.
• Cathode rays appeared to be a constituent of all
• matter and, thus, appeared to be a
  sub-atomic
• particle.
• Cathode rays had a negative charge.
• Cathode rays have a charge-to-mass ratio
• of 1.7588 x 108 C/g.

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ATOMIC STRUCTURE
R. A. Millikan - Measured the charge of the
electron.
In his famous oil-drop experiment, Millikan was
able to determine the charge on the electron
independently of its mass. Then using Thompsons
charge-to-mass ratio, he was able to calculate
the mass of the electron.
e 1.602 10 x 10-19 coulomb e/m 1.7588 x 108
coulomb/gram m 9.1091 x 10-28 gram
Goldstein - Conducted positive ray experiments
that lead to the identification of the proton.
The charge was found to be identical to that of
the electron and the mass was found to be 1.6726
x 10-24 g.
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ATOMIC STRUCTURE
Ernest Rutherford - Developed the nuclear
model of the atom.
The Plum Pudding Model of the atom
A smeared out pudding of positive charge
with negative electron plums imbedded in it.

Electrons
The Metal Foil Experiments
Fluorescent Screen
a-particles
Radioactive Material in Pb box.
Metal Foil
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ATOMIC STRUCTURE
If the plum pudding model is correct, then all
of the massive a-particles should pass right
through without being deflected.
In fact, most of the a - particles DID pass
right through. However, a few of them were
deflected at high angles, disproving the plum
pudding model.
Rutherford concluded from this that the atom
con- sisted of a very dense nucleus containing
all of the positive charge and most of the mass
surrounded electrons that orbited around the
nucleus much as the planets orbit around the sun.
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ATOMIC STRUCTURE

• Problems with the Rutherford Model
• It was known from experiment and electromagnetic
• theory that when charges are accelerated, they
• continuously emit radiation, i.e., they loose
  energy
• continuously. The orbiting electrons in the
  atom
• were, obviously, not doing this.

Planck

• Atomic spectra and blackbody radiation
• were known to be DIScontinuous.

Bohr

• The atoms were NOT collapsing.

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ATOMIC STRUCTURE
Atomic Spectra - Since the 19th century, it
had been known that when elements are heated
until they emit light (glow) they emit that light
only at discrete frequencies, giving a line
spectrum.
-

Hydrogen Gas
Line Spectrum
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ATOMIC STRUCTURE
When white light is passed through a sample
of the vapor of an element, only discrete
frequencies are absorbed, giving a absorption ban
spectrum. These frequencies are identical to
those of the line spectrum of the same element.
For hydrogen, the spectroscopists of the
19th Century found that the lines were related by
the Rydberg equation
n/c R(1/m2) - (1/n2)
n frequency
R Rydberg Constant
c speed of light
m 1, 2, 3, .
n (m1), (m2), (m3), .
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ATOMIC STRUCTURE
Max Planck - In 1900 he was investigating the
nature of black body radiation and tried to
interpret his findings using accepted theories of
electromagnetic radiation (light). He was NOT
successful since these theories were based on the
assumption that light had WAVE characteristics. T
o solve the problem he postulated that light
was emitted from black bodies in discrete packets
he called quanta. Einstein later called
them photons. By assuming that the atoms of
the black body emitted energy only at discrete
frequencies, he was able to explain black body
radiation.
E hn hn/l
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ATOMIC STRUCTURE
Both spectroscopy and black body
radiation indicated that atoms emitted energy
only at discrete frequencies or energies rather
than continuously.
Is light a particle or a wave??
Why do atoms emit only discrete energies?
What actually happens when light interacts with
matter?
What was wrong with Rutherfords Model?
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ATOMIC STRUCTURE

• Niels Bohr - Bohr corrected Rutherfords model
• of the atom by formulating the following
  postulates
• Electrons in atoms move only in discrete orbits
• around the nucleus.
• When in an orbit, the electron does NOT emit
• energy.
• They may move from one orbit to another but are
• NEVER residing in between orbits.
• When an electron moves from one orbit to
• another, it absorbs or emits a photon of light
  with a
• specific energy that depends on the distance
  between
• the two orbits.

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ATOMIC STRUCTURE
Balmer Series
(Visible)
Lyman Series

Paschen Series
(UV)
(IR)
The Bohr Model of the Atom
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ATOMIC STRUCTURE

• The lowest possible energy state for an electron
• is called the GROUND STATE. All other states
• are called EXCITED STATES.

En (- 2.179 x 10-18 J)/n2
Ephoton Efinal - Einitial
Ephoton (- 2.179 x 10-18 J)/n2final
-(- 2.179 x 10-18 J)/n2initial
- 2.179 x 10-18 J(1/n2final) - (1/n2initial)
Does this equation look familiar?
n/c R(1/m2) - (1/n2)
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ATOMIC STRUCTURE
Niels Bohr won the Nobel Prize for his work.
However, the model only worked perfectly
for hydrogen. What about all of those other
elements??
Louis de Broglie - Thought that if light, which
was thought to have wave characteristics, could
also have particle characteristics, then perhaps
electrons, which were thought to be particles,
could have characteristics of waves.
l h/mv where mv is momentum
An electron in an atom was a standing wave!
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ATOMIC STRUCTURE
Werner Heisenberg - Developed the
uncertainty principle It is impossible to
make simultaneous and exact measurements of both
the position (location) and the momentum of a
sub-atomic particle such as an electron.
(Dx)(Dp) gt h/2p
Our knowledge of the inner workings of atoms
and molecules must be based on probabilities
rather than on absolute certainties.
Erwin Schödinger - Developed a form of
quantum mechanics known as Wave Mechanics.
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ATOMIC STRUCTURE

• Wave Function - A mathematical function
  associated
• with each possible state of an electron in an
  atom or
• molecule.
• It can be used to calculate the energy of an
• electron in the state
• the average and most probable distance from the
• nucleus
• the probability of finding the electron in any
• specified region of space.

Y
Y
Y
Y
Y
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ATOMIC STRUCTURE
Quantum Numbers
Principle Quantum Number, n - An integer greater
than zero that represents the principle energy
level or shell that an electron occupies.
Energy of orbitals n Level Shell n2 1
1st K 1 2 2nd L 4 3 3rd
M 9 4 4th N 16 etc. etc.
etc. etc.
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ATOMIC STRUCTURE
Azimuthal Quantum Number, l - The quantum number
that designates the subshell an
electron occupies. It is an indicator of the
shape of an orbital in the subshell. It has
integer values from 0 to n-1.
l 0, 1, 2, 3, 4, , n - 1
s p d f g.
Magnetic Quantum Number, ml - The quantum number
that determines the behavior of an electron in a
magnetic field. It has integer values from -l
to l including 0.
ml -l, , -3, -2, -1, 0, 1, 2, 3, , l
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ATOMIC STRUCTURE
Orbital of n l Name
ml Orbitals 1 0 1s 0
1 2 0 2s 0 1 1
2p -1, 0, 1 3 3 0 3s 0
1 1 3p -1, 0, 1
3 2 3d -2, -1, 0, 1, 2
5 etc. etc. etc. etc. etc.
Spin Quantum Number, ms - The quantum number that
designates the orientation of an electron in a
magnetic field. It has half-integer values, ½
or -½.
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ATOMIC STRUCTURE
So what do atoms look like?
A. Interpretation of Y The probability of
finding an electron in a small volume of space
centered around some point is proportional to
the value of Y2 at that point.
B. Electron Probability Density vs. r C. Dot
Density Representation Imagine super- imposing
millions of photographs taken of an electron in
rapid succession. D. Radial Densities
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Chapter 8Electron Configuration andChemical
Periodicity
Read/Study Chapter 8 Suggested Problems
Sample Problems 8.1 - 8.8 Follow-up Problems
8.1 - 8.8 End-of-Chapter Problems At least
every 3rd problem. ChemSkill Builder Units
9 11
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ATOMIC STRUCTURE
Electron Configuration A. Many-electron atom
An atom that contains two or more electrons. B.
Problems with the Bohr model 1. It assumed
quantization of the energy levels in
hydrogen. 2. It failed to describe or predict
the spectra of more complicated atoms.
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C. What are the differences in electron
energy levels in hydrogen vs. more complicated
atoms?
3s 3p 3d
Energy
2s
2p
Ground State Hydrogen Atom
1s
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Splitting of the Degeneracy
2p
2s
2p
2s
Energy
1s
1s
Li
H
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Splitting of the Degeneracy
1. In hydrogen, all subshells and orbitals in
a given principal energy level have the same
energy. They are said to be Degenerate. 2. In
many-electron atoms, s-orbitals have lower energy
than p-orbitals which have lower energy than
d-orbitals which have lower energy than
f-orbitals, etc., etc. 3. Reason Complex
electrostatic interactions.
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-
-
-
-
-

-

Hydrogen

Helium
Lithium
A. Shielding Effect - A decrease in the nuclear
force of attraction for an electron caused by the
presence of other electrons in underlying
orbitals.
B. Effective Nuclear Charge - A positive
charge that may be less than the atomic number.
It is the charge felt by outer electrons due to
shielding by electrons in underlying orbitals.
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The Pauli Exclusion Principle - No two electron
in the same atom can have the same four
quantum numbers.
H e- ? H -
Quantum Electron 1 Electron 2 Number
n 1 1 l 0 0 ml 0 0
ms 1/2 -1/2
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The Aufbau Principle - A procedure for building
up the electronic configuration of many-electron
atoms wherein each electron is added
consecutively to the lowest energy orbital
available, taking into account the Pauli
exclusion principle. Order of Filling -
1s 2s 2p 3s 3p 4s 3d 4p 5s
Increasing Energy
1s 2s 2p 3s 3p 3d 4s 4p 4d 4f 5s 5p 5d
5f 5g
mnemonic device
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• Designating Electron Configurations -
• Standard Designation

H 1s1 He 1s2
Li 1s2 2s1 Be 1s2 2s2
B 1s2 2s2 2p1 C 1s2 2s2 2p2

• Orbital Diagram Designation

H He
Li Be
B C
1s
2s
1s
1s
2s
2p
1s
2s
2p
1s
2s
1s
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• Core Designation - A designation of electronic
• configuration wherein the outer shell electrons
• are shown along with the core configuration of
• the closest previous noble gas.

Li Na K Rb
He 2s1
He 2s2
Be Mg Ca Sr
Ne 3s1
Ne 3s2
Ar 4s1
Ar 4s2
Kr 5s1
Kr 5s2
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Hunds Rule of Maximum Multiplicity -
Electrons occupy a given subshell singly and with
parallel spins until each orbital in the subshell
has one electron.
Electrons try to stay as far apart as possible

• Elevator Analogy

• Bus Seat Analogy

He 2s2 2p1
He
B C N
He 2s2 2p2
He
He 2s2 2p3
He
2s
2p
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• The Structure of the Periodic Table
• Historical Development - Dimitri Mendeleev and
• Lothar Meyer independently found that when the
• elements are ordered according to their atomic
  masses,
• similar properties recur periodically. Were they
  right?
• The Periodic Law - The properties of the
  elements
• are periodic functions of their atomic number.
• Physical Structure of the Table

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• Electronic Configuration and the Periodic Table
• s-Block Elements
• p-Block Elements
• d-Block Elements
• f-Block Elements

Assignment Write the electron configuration
using all three types of designation for lead
(Pb).
Electronic Configuration for positive ions
(cations) - Cations are formed by removing
electrons in order of decreasing n value.
Electrons with the same n value are removed in
order of decreasing l value.
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• Electronic Configuration and the Periodic Table
• s-Block Elements
• p-Block Elements
• d-Block Elements
• f-Block Elements

Assignment Write the electron configuration
using all three types of designation for lead
(Pb).
Pb 1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2 4d10 5p6
6s2 4f14 5d10 6p2 Pb Xe 6s2 4f14 5d10 6p2
(You do the orbital diagram designation!)
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• The properties of the elements are determined in
• large measure by their Atomic Number and their
• Electron Configuration.
• Paramagnetism - A property that arises from
• unpaired electrons in an atom or molecule. It
• is identified by the fact that when the element
• is placed in a magnetic field in a magnetic
• susceptibility experiment, the atom or molecule
• is drawn into the field.

Assignment Name the elements of the first
40 elements in the Periodic Table that are
diamagnetic.
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• Atomic Size -

Atomic radii are considered to be 1/2 of
the average distance between centers of
identical atoms that are touching each other.
This will vary with the chemical environment the
atom is in.
142 pm
154 pm
Fluorine
Diamond
C - 77 pm F - 71 pm
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Trends in Atomic Radii
1. Atomic radii increase from top to bottom in
a family or group.
The number of electrons and the nuclear charge
are increasing! - Tends to shrink atom.
But extra electron are added to new shells
that are further from the nucleus and
more effectively shielded from the nucleus -
Tends to make the atom larger.
The Winner!!
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2. Atomic radii decrease from left to
right across a row or period.
The number of electrons and the nuclear charge
are increasing! - Tends to shrink atom.
The electrons are being added to the same shell
and are not well shielded and thus, the atoms get
smaller.
3. Summary of trends Down a Group -
Larger Across a Period - Smaller
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What Affects Atomic/Ionic Sizes?

• The Charge on the Nucleus
• Shielding - This reduces the actual nuclear
• charge resulting in an effective nuclear
• charge.

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4. Some Exceptions Al - Ga Eu Yb The
Lanthanide Contraction

• Ionic Size -
• Based on the internuclear distance of cations and
• anions in ionic crystals.
• Not easy to determine how to apportion this
• distance between the cation and the anion.

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• Cations - Monatomic cations are smaller than
• their parent atoms.
• The whole outer shell is typically removed.
• The effective nuclear charge is increased.

Na atom 186 nm
Na ion 102 nm
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• Anions - Monatomic anions are larger than
• their parent atoms.
• The extra electrons are typically added to
• the same shell where they are repelled by
• the other electrons already present, making
• the ion bigger than its parent atom.

F Atom 71 nm
Fluoride Ion 136 nm
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• Ionization Energy - The energy required to
• remove an electron from a gaseous ground-
• state atom or ion.

A. First Ionization Energy - The energy required
to remove the most loosely bound electron from
the valence shell. B. Second Ionization Energy
- The energy required to remove the second
electron after the first one is gone. C. Third
Ionization Energy - Etc., Etc., Etc.
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Li (g) Li e- Li Li2 e-
IE1 520 kJ/mol IE2 7298 kJ/mol
Na (g) Na e-
IE1 496 kJ/mol IE2 4564 kJ/mol IE3
6918 kJ/mol
Na Na2 e-
Na2 Na3 e-
Mg (g) Mg e- Mg Mg2
e- Mg2 Mg3 e-
IE1 737 kJ/mol IE2 1447 kJ/mol IE3
7738 kJ/mol
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• Electron Affinity - The energy absorbed when
• an electron is added to a gaseous ground-state
• atom or ion. It has the same sign as the D H of
• the process.

Cl (g) e - Cl -
D H - 349 kJ/mol E.A. - 349 kJ/mol
Some other textbooks use a different
sign convention for the E.A. You need to be
aware of that when you are reading about this
topic. In those texts, the electron affinity for
a chlorine atom would be 349 kJ/mol!

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F (g) e - F - E.A. -
328 kJ/mol
O (g) e - O - E.A. -
141 kJ/mol
O - e - O 2- E.A.
880 kJ/mol
O (g) 2 e - O 2- E.A. 739
kJ/mol
DH 739 kJ/mol
So then why does oxygen usually have a -2
oxidation state instead of a -1 oxidation state
(Oxides are more common than peroxides)???
Na (g) e - Na - E.A. -
53 kJ/mol
D H - 53 kJ/mol