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Chapter 6
Electronic Structure of Atoms
Waves
• To understand the electronic structure of atoms,
one must understand the nature of
electromagnetic radiation.
• The distance between corresponding points on
adjacent waves is the wavelength ().
• The amplitude of a wave is one-half the distance
between crest and trough.
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Waves
• The number of waves
passing a given point per
unit of time is the
frequency ().
• For waves traveling at the
same velocity, the longer
the wavelength, the
smaller the frequency.
All electromagnetic radiation
travels at the same velocity:
the speed of light (c),
3.00  108 m/s.
Therefore
c = 
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The Nature of Energy
• A mystery in the late 19th
century was that of
blackbody radiation.
• The wave nature of light
does not explain how an
object can glow when its
temperature increases.
• Max Planck explained it
by assuming that energy
comes in packets called
quanta.
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The Nature of Energy
• Einstein used this assumption to
explain the photoelectric effect.
• He concluded that energy is
proportional to frequency:
E = h
where h is Planck’s constant
(=6.626  10−34 J-s)
• Therefore, if one knows the
wavelength of light, one can
calculate the energy in one
photon, or packet, of that light:
c =  and E = h
E= hc/
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The Nature of Energy
Another mystery in the
early 20th century involved
the emission spectra
observed from energy
emitted by atoms and
molecules.
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The Nature of Energy
•
Niels Bohr adopted Planck’s
assumption and explained these
phenomena in this way:
1. Electrons in an atom can only
occupy certain orbits
(corresponding to certain energies).
2. Electrons in permitted orbits have
specific, “allowed” energies.
3. Energy is only absorbed or emitted
in such a way as to move an
electron from one “allowed”
energy state to another; the energy
is defined by
E = h
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The Nature of Energy
The energy absorbed or emitted from
the process of electron promotion or
demotion can be calculated by the
equation:
E = −RH
(
1
nf2
-
1
ni2
)
where RH is the Rydberg constant,
2.18  10−18 J, and ni and nf are the
initial and final energy levels of the
electron.
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We can also find the energy
associated with a specific
energy level and use the
difference to find the
energy emitted or absorbed
upon transition:
En= -2.178x 10-18
n2
Once the energy is known,
we can find frequency and
wavelength!
Wave-Particle Duality
• Einstein’s explanation of the photoelectric
effect led to the concept of photons of light.
• Louis de Broglie proposed that if light can have
properties (could behave as if it were a stream
of particles), matter should exhibit wave
properties.
• He demonstrated that the relationship
between mass and wavelength was
h
 = mv
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The Uncertainty Principle
• Werner Heisenberg showed that the more precisely
the momentum of a particle is known, the less
precisely its location is known.
• For large objects, we can calculate position and
momentum with great accuracy. For electrons we
are limited.
• For large objects, the uncertainty is extremely small!
• Our uncertainty of the whereabouts of an electron is
often greater than the size of the atom itself!
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Quantum Mechanics
• Erwin Schrödinger developed a
mathematical treatment into
which both the wave and
particle nature of matter could
be incorporated.
• It is known as quantum
mechanics.
• The square of the wave
equation, 2, gives a
probability density map of
where an electron has a certain
statistical likelihood of being at
any given instant in time.
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Quantum Numbers
• Solving the wave equation gives a set of wave
functions, or orbitals, and their corresponding
energies.
• Each orbital describes a spatial distribution of
electron density.
• An orbital is described by a set of three
quantum numbers.
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Principal Quantum Number (n)
• The principal quantum number, n, describes
the energy level on which the orbital resides;
this represents the electron’s distance from
the nucleus.
• The values of n are integers ≥ 1.
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Angular Momentum or Azimuthal
Quantum Number (l)
• This quantum number defines the shape of
the orbital.
• Allowed values of l are integers ranging
from 0 to n − 1.
• We use letter designations to communicate
the different values of l and, therefore, the
shapes and types of orbitals. (s, p, d and f)
Value of l
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Magnetic Quantum Number (ml)
• The magnetic quantum number describes
the three-dimensional orientation of the
orbital.
• Allowed values of ml are integers ranging
from -l to l:
• If l=0, ml=0
if l=1, ml = -1, 0,1
• Therefore, on any given energy level, there
can be up to 1 s orbital, 3 p orbitals, 5 d
orbitals, 7 f orbitals, etc.
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p orbitals
d orbitals
s orbitals are
spherical in shape.
(The radius of the
sphere increases
with the value of
n.)
Energies of Orbitals
• For a one-electron hydrogen
atom, orbitals on the same
energy level have the same
energy.
That is, they are degenerate.
• As the number of electrons
increases, though, so does the
repulsion between them.
• Therefore, in many-electron
atoms, orbitals on the same
energy level are no longer
degenerate.
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Spin Quantum Number, ms
• In the 1920s, it was
discovered that two
electrons in the same orbital
do not have exactly the same
energy.
• The “spin” of an electron
describes its magnetic field,
which affects its energy. This
led to a fourth quantum
number, the spin quantum
number, ms.
• The spin quantum number
has only 2 allowed values:
+1/2 and −1/2.
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Pauli Exclusion Principle
• No two electrons in the
same atom can have
exactly the same energy.
• Therefore, no two
electrons in the same
atom can have identical
sets of quantum numbers.
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Electron Configurations
• This shows the distribution of all
electrons in an atom.
• Each component consists of
– A number denoting the energy level,
– A letter denoting the type of orbital,
– A superscript denoting the number of
electrons in those orbitals.
Bohr notation:
2-8-3
Spectroscopic notation
1s2s22p63s23p1
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Orbital Diagrams
• Each box in the diagram
represents one orbital.
• Half-arrows represent the
electrons.
• The direction of the
arrow represents the
relative spin of the
electron.
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Hund’s rule of maximum multiplicity
If there is more than one orbital with the same energy
(degenerate) then one electron is placed into each orbital
before any pairing takes place. All three 2p orbitals have
the same energy and are said to be degenerate. If there
are four electrons to be placed into the 2p orbitals one
would enter the x, one would enter the y and one would
enter the z before any were paired in the x, y or z.
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Using the Periodic Table
• Different blocks on the
periodic table (shaded in
different colors in this
chart) correspond to
different types of
orbitals.
• In the s and p block,
electrons are added to
PEL = n.
• In the d block, to n- 1
• In the f block, to n -2
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Some Anomalies
For instance, the
electron configuration
for copper is
[Ar] 4s1 3d5
rather than the
expected
[Ar] 4s2 3d4.
(this occurs because the
4s and 3d orbitals are
very close in energy)
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Noble gas core method
In this method the electronic configuration is
determined by writing the previous noble gas in
square brackets and then filling orbitals as before.
Ex: Phosphorus becomes:
[Ne] 3s2 3p3
Nickel becomes:
[Ar] 3d84s2
Photoelectron Spectroscopy (PES)
• Used to confirm the number of electrons and
the location of the those electrons in an atom
• Using high energy UV or X-ray radiation,
electrons are removed from a neutral atom
• By knowing the kinetic energy of the electron
removed and the energy of the photon used
to remove it, the electron’s binding energy can
be calculated
Interpreting PES data
The size of the peak is a
measure of the intensity of the
energy, which is directly related
to the number of electrons
1s2
WHAT ELEMENT IS
REPRESENTED BY THIS PES?
2p6
2s2
The x-axis is the energy needed to remove the electron and is labeled
from high energy (close to the nucleus) to lower energy (farther away).
Chapter 7
Periodic Properties of The Elements
Development of Periodic Table
Dmitri Mendeleev
and Lothar Meyer
independently
came to the same
conclusion about
how elements
should be
grouped.
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Development of Periodic Table
Mendeleev, for instance, predicted the discovery of
germanium (which he called eka-silicon) as an
element with an atomic weight between that of zinc
and arsenic, but with chemical properties similar to
those of silicon.
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Development of Periodic Table
• Elements in the same
group generally have
similar chemical
properties.
• Physical properties are
not necessarily similar,
however.
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Effective Nuclear Charge
• In a many-electron atom,
electrons are both
attracted to the nucleus
and repelled by other
electrons.
• The nuclear charge that
an electron experiences
depends on both factors.
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Effective Nuclear Charge
The effective nuclear
charge, Zeff, is found this
way:
Zeff = Z − S
where Z is the atomic
number and S is a
screening constant,
usually close to the
number of inner
electrons.
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Atomic Radius
The bonding atomic
radius is defined as
one-half of the
distance between
covalently bonded
nuclei.
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Sizes of Atoms
Bonding atomic radius
tends to…
…decrease from left to
right across a row
(due to increasing Zeff).
…increase from top to
bottom of a column
(due to increasing value of
n).
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Sizes of Ions
• Ionic size depends
upon:
– The nuclear charge.
– The number of
electrons.
– The orbitals in which
electrons reside.
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Sizes of Ions
• Cations are smaller
than their parent
atoms.
The outermost electron is
removed and repulsions
between electrons are
reduced.
• Anions are larger than
their parent atoms.
Electrons are added
and repulsions
between electrons are
increased.
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Sizes of Ions
• In an isoelectronic series, ions have the same
number of electrons.
• Ionic size decreases with an increasing nuclear
charge.
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Ionization Energy
• The ionization energy is the amount of
energy required to remove an electron
from the ground state of a gaseous atom or
ion.
– The first ionization energy is that energy
required to remove first electron.
– The second ionization energy is that energy
required to remove second electron, etc.
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Ionization Energy
• It requires more energy to remove each successive
electron.
• When all valence electrons have been removed, the
ionization energy takes a giant leap.
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Trends in First Ionization Energies
• As one goes down a
column, less energy is
required to remove the
first electron.
– For atoms in the same
group, Zeff is essentially
the same, but the
valence electrons are
farther from the nucleus.
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Trends in First Ionization Energies
• Generally, as one goes
across a row, it gets
harder to remove an
electron.
– As you go from left to
right, Zeff increases.
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Trends in First Ionization Energies
However, there are
two apparent
discontinuities in this
trend.
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Trends in First Ionization Energies
• The first occurs between
Groups IIA and IIIA.
• In this case the electron
is removed from a porbital rather than an sorbital.
– The electron removed is
farther from nucleus.
– There is also a small
amount of repulsion by
the s electrons.
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Trends in First Ionization Energies
• The second occurs
between Groups VA and
VIA.
– The electron removed
comes from doubly
occupied orbital.
– Repulsion from the other
electron in the orbital aids
in its removal.
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Electron Affinity
Electron affinity is the energy change accompanying the
addition of an electron to a gaseous atom:
Cl + e−  Cl−
In general, electron
affinity becomes more
exothermic as you go
from left to right
across a row.
There are two discontinuities in this trend.
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Trends in Electron Affinity
• The first occurs
between Groups IA and
IIA.
– The added electron
must go in a p-orbital,
not an s-orbital.
– The electron is farther
from nucleus and feels
repulsion from the selectrons.
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Trends in Electron Affinity
• The second occurs
between Groups IVA
and VA.
– Group VA has no empty
orbitals.
– The extra electron must
go into an already
occupied orbital,
creating repulsion.
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Properties of Metal, Nonmetals,
and Metalloids
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