Download Chapter 6 Electronic Structure of Atoms

Lecture Presentation
Chapter 6
Electronic Structure
of Atoms
© 2012 Pearson Education, Inc.
John D. Bookstaver
St. Charles Community College
Cottleville, MO
The Beginnings of Quantum Mechanics
• Until the beginning of the 20th century it was believed
that all physical phenomena were deterministic
• Work done at that time by many famous physicists
discovered that for sub-atomic particles, the present
condition does not determine the future condition
 Albert Einstein, Neils Bohr, Louis de Broglie, Max Planck, Werner
Heisenberg, P. A. M. Dirac, and Erwin Schrödinger
• Quantum mechanics forms the foundation of
chemistry – explaining the periodic table and the
behavior of the elements in chemical bonding – as
well as providing the practical basis for lasers,
computers, and countless other applications
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The Behavior of the Very Small
• Electrons are incredibly small
a single speck of dust has more electrons than the
number of people who have ever lived on earth
• Electron behavior determines much of the
•
behavior of atoms
Directly observing electrons in the atom is
impossible, the electron is so small that
observing it changes its behavior
even shining a light on the electron would affect it
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A Theory that Explains Electron Behavior
• The quantum-mechanical model explains the
•
manner in which electrons exist and behave in
atoms
It helps us understand and predict the properties
of atoms that are directly related to the behavior
of the electrons
 why some elements are metals and others are nonmetals
 why some elements gain one electron when forming an
anion, whereas others gain two
 why some elements are very reactive while others are
practically inert
 and other periodic patterns we see in the properties of the
elements
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The Nature of Light:
Its Wave Nature
• Light is a form of electromagnetic radiation
composed of perpendicular oscillating waves, one
for the electric field and one for the magnetic field
an electric field is a region where an electrically charged
particle experiences a force
a magnetic field is a region where a magnetized particle
experiences a force
• All electromagnetic waves move through space
at the same, constant speed
3.00 x 108 m/s in a vacuum = the speed of light, c
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Electromagnetic Radiation
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Speed of Energy Transmission
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Characterizing Waves
• The amplitude is the height of the wave
the distance from node to crest
or node to trough
the amplitude is a measure of how intense the light
is – the larger the amplitude, the brighter the light
• The wavelength (l) is a measure of the
distance covered by the wave
the distance from one crest to the next
or the distance from one trough to the next, or the
distance between alternate nodes
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Wave Characteristics
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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 (l).
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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.
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Amplitude & Wavelength
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Characterizing Waves
• The frequency () is the number of waves that
pass a point in a given period of time
the number of waves = number of cycles
units are hertz (Hz) or cycles/s = s−1
1 Hz = 1 s−1
• The total energy is proportional to the
amplitude of the waves and the frequency
the larger the amplitude, the more force it has
the more frequently the waves strike, the more total
force there is
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The Relationship Between
Wavelength and Frequency
• For waves traveling at the same speed, the
•
shorter the wavelength, the more frequently
they pass
This means that the wavelength and
frequency of electromagnetic waves are
inversely proportional
 because the speed of light is constant, if we know
wavelength we can find the frequency, and vice versa
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Example 7.1: Calculate the wavelength of red
light with a frequency of 4.62 x 1014 s−1
Given:  = 4.62 x 1014 s−1
Find: l, (nm)
Conceptual
Plan:
 (s−1)
l (m)
l (nm)
Relationships: l∙ = c, 1 nm = 10−9 m
Solve:
Check: the unit is correct, the wavelength is
appropriate for red light
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Practice – Calculate the wavelength of a radio
signal with a frequency of 100.7 MHz
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Practice – Calculate the wavelength of a radio
signal with a frequency of 100.7 MHz
Given:  = 100.7 MHz
Find: l, (m)
Conceptual  (MHz)
Plan:
 (s−1)
l (m)
Relationships: l∙ = c, 1 MHz = 106 s−1
Solve:
Check: the unit is correct, the wavelength is
appropriate for radiowaves
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Color
• The color of light is determined by
its wavelength
 or frequency
• White light is a mixture of all the
colors of visible light
 a spectrum
 RedOrangeYellowGreenBlueViolet
• When an object absorbs some
of the wavelengths of white light
and reflects others, it appears
colored
 the observed color is predominantly
the colors reflected
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Electromagnetic Radiation
• All electromagnetic radiation travels at the same
•
velocity: the speed of light (c),
3.00  108 m/s.
Therefore,
c = l
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The Electromagnetic Spectrum
• Visible light comprises only a small fraction of
all the wavelengths of light – called the
electromagnetic spectrum
• Shorter wavelength (high-frequency) light has
higher energy
radiowave light has the lowest energy
gamma ray light has the highest energy
• High-energy electromagnetic radiation can
potentially damage biological molecules
ionizing radiation
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Types of Electromagnetic Radiation
• Electromagnetic waves are classified by their
•
•
•
•
•
•
•
wavelength
Radiowaves = l > 0.01 m
Microwaves = 10−4 < l < 10−2 m
Infrared (IR)
far = 10−5 < l < 10−4 m
middle = 2 x 10−6 < l < 10−5 m
near = 8 x 10−7< l < 2 x 10−6 m
Visible = 4 x 10−7 < l < 8 x 10−7 m
ROYGBIV
Ultraviolet (UV)
near = 2 x 10−7 < l < 4 x 10−7 m
far = 1 x 10−8 < l < 2 x 10−7 m
X-rays = 10−10 < l < 10−8m
Gamma rays = l < 10−10
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low frequency
and energy
high frequency
and energy
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The Nature of Energy
The wave nature of light
does not explain how
an object can glow
when its temperature
increases.
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Electronic
Structure
of Atoms
The Nature of Energy
Max Planck explained it by assuming that
energy comes in packets called quanta.
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Electronic
Structure
of Atoms
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.
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Electronic
Structure
of Atoms
The Nature of Energy
• Therefore, if one knows the
wavelength of light, one
can calculate the energy in
one photon, or packet, of
that light:
c = l
E = h
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Electronic
Structure
of Atoms
The Nature of Energy
Another mystery in
the early twentieth
century involved the
emission spectra
observed from
energy emitted by
atoms and
molecules.
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Electronic
Structure
of Atoms
The Nature of Energy
• For atoms and
molecules, one does
not observe a
continuous spectrum,
as one gets from a
white light source.
• Only a line spectrum
of discrete
wavelengths is
observed.
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Electronic
Structure
of Atoms
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).
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Electronic
Structure
of Atoms
The Nature of Energy
•
Niels Bohr adopted Planck’s
assumption and explained
these phenomena in this
way:
2. Electrons in permitted orbits
have specific, “allowed”
energies; these energies will
not be radiated from the atom.
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Electronic
Structure
of Atoms
The Nature of Energy
•
Niels Bohr adopted Planck’s
assumption and explained
these phenomena in this
way:
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
Electronic
Structure
E = h
of Atoms
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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 = −hcRH (
1
1
n f2
ni2
)
where RH is the Rydberg
constant, 1.097  107 m−1, and ni
and nf are the initial and final
energy levels of the electron.
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Electronic
Structure
of Atoms
The Wave Nature of Matter
• Louis de Broglie posited
that if light can have
material properties,
matter should exhibit
wave properties.
• He demonstrated that the
relationship between
mass and wavelength
was
h
l = mv
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Electronic
Structure
of Atoms
The Uncertainty Principle
Heisenberg showed
that the more
precisely the
momentum of a
particle is known,
the less precisely is
its position is known:
(x) (mv) 
h
4
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Electronic
Structure
of Atoms
The Uncertainty Principle
In many cases, our
uncertainty of the
whereabouts of an
electron is greater
than the size of the
atom itself!
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Electronic
Structure
of Atoms
Electron Energy
• for an electron with a given energy, the best we
can do is describe a region in the atom of high
probability of finding it – called an orbital
– a probability distribution map of a region where the
electron is likely to be found
– distance vs. y2
Electronic
Structure
35Atoms
of
Quantum Mechanics
• Erwin Schrödinger
developed a
mathematical treatment
into which both the
wave and particle nature
of matter could be
incorporated.
• This is known as
quantum mechanics.
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Electronic
Structure
of Atoms
Quantum Mechanics
• The wave equation is
designated with a lowercase
Greek psi (y).
• The square of the wave
equation, y2, 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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Electronic
Structure
of Atoms
Schrödinger’s Equation
• Schödinger’s Equation allows us to calculate
•
•
the probability of finding an electron with a
particular amount of energy at a particular
location in the atom
Solutions to Schödinger’s Equation produce
many wave functions, Y
A plot of distance vs. Y2 represents an orbital,
a probability distribution map of a region where
the electron is likely to be found
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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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Electronic
Structure
of Atoms
Wave Function, y
• calculations show that the size, shape and
orientation in space of an orbital are determined
be three integer terms in the wave function
• these integers are called quantum numbers
principal quantum number, n
angular momentum quantum number, l
magnetic quantum number, ml
40
Principal Quantum Number (n)
• The principal quantum number, n,
describes the energy level on which the
orbital resides.
• The values of n are integers ≥ 1.
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Electronic
Structure
of Atoms
Angular Momentum 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.
Electronic
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Structure
of Atoms
Angular Momentum Quantum
Number (l)
Value of l
0
1
2
3
Type of orbital
s
p
d
f
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Electronic
Structure
of Atoms
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:
−l ≤ ml ≤ l
• Therefore, on any given energy level, there
can be up to 1 s orbital, 3 p orbitals, 5 d
orbitals, 7 f orbitals, and so forth.
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Electronic
Structure
of Atoms
Magnetic Quantum Number (ml)
• Orbitals with the same value of n form a shell.
• Different orbital types within a shell are subshells.
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Electronic
Structure
of Atoms
The Shapes of Atomic Orbitals
• the l quantum number primarily determines the
shape of the orbital
• each value of l is called by a particular letter that
designates the shape of the orbital
s orbitals are spherical
p orbitals are like two balloons tied at the knots
d orbitals are mainly like 4 balloons tied at the knot
f orbitals are mainly like 8 balloons tied at the knot
46
s Orbitals
• The value of l for s orbitals is 0.
• They are spherical in shape.
• The radius of the sphere increases with the
value of n.
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Electronic
Structure
of Atoms
l = 0, the s orbital
• each principal energy state
has 1 s orbital
• lowest energy orbital in a
principal energy state
• spherical
• number of nodes = (n – 1)
48
s Orbitals
Observing a graph of
probabilities of finding an
electron versus distance
from the nucleus, we see
that s orbitals possess n
− 1 nodes, or regions
where there is 0
probability of finding an
Electronic
electron.
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Structure
of Atoms
2s and 3s
2s
n = 2,
l=0
3s
n = 3,
l=0
50
p Orbitals
• The value of l for p orbitals is 1.
• They have two lobes with a node between
them.
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Electronic
Structure
of Atoms
l = 1, p orbitals
• each principal energy state above n = 1 has 3
p orbitals
– ml = -1, 0, +1
• each of the 3 orbitals point along a different
axis
– px, py, pz
• 2nd lowest energy orbitals in a principal
energy state
• two-lobed
• node at the nucleus
Electronic
Structure
52Atoms
of
p orbitals
Electronic
Structure
53Atoms
of
l = 2, d orbitals
• each principal energy state above n = 2 has 5 d orbitals
 ml = -2, -1, 0, +1, +2
• 4 of the 5 orbitals are aligned in a different plane
 the fifth is aligned with the z axis, dz squared
 dxy, dyz, dxz, dx squared – y squared
• 3rd lowest energy orbitals in a principal energy state
• mainly 4-lobed
 one is two-lobed with a toroid
• planar nodes
 higher principal levels also have spherical nodes
54
d Orbitals
• The value of l for a
d orbital is 2.
• Four of the five d
orbitals have 4
lobes; the other
resembles a p
orbital with a
doughnut around
the center.
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Electronic
Structure
of Atoms
d orbitals
56
l = 3, f orbitals
• each principal energy state above n = 3 has 7 d orbitals
 ml = -3, -2, -1, 0, +1, +2, +3
• 4th lowest energy orbitals in a principal energy state
• mainly 8-lobed
 some 2-lobed with a toroid
• planar nodes
 higher principal levels also have spherical nodes
57
f orbitals
58
Energies of Orbitals
• For a one-electron
hydrogen atom,
orbitals on the same
energy level have
the same energy.
• That is, they are
degenerate.
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Electronic
Structure
of Atoms
Energies of Orbitals
• As the number of
electrons increases,
though, so does the
repulsion between
them.
• Therefore, in manyelectron atoms,
orbitals on the same
energy level are no
longer degenerate.
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Electronic
Structure
of Atoms
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.
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Electronic
Structure
of Atoms
Spin Quantum Number, ms
• 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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Electronic
Structure
of Atoms
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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Electronic
Structure
of Atoms
Electron Configurations
5
4p
• This term shows the
distribution of all
electrons in an atom.
• Each component
consists of
– A number denoting the
energy level,
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Electronic
Structure
of Atoms
Electron Configurations
5
4p
• This term 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,
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Electronic
Structure
of Atoms
Electron Configurations
5
4p
• This term 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.
Electronic
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Structure
of Atoms
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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Electronic
Structure
of Atoms
Hund’s Rule
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“For
degenerate
orbitals, the
lowest
energy is
attained
when the
number of
electrons with
the same
spin is
maximized.”
Electronic
Structure
of Atoms
Energy Shells and Subshells
Electronic
Structure
69Atoms
of
Periodic Table
• We fill orbitals in increasing order of energy.
• Different blocks on the periodic table (shaded
in different colors in this chart) correspond to
different types of orbitals.
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Electronic
Structure
of Atoms
Some Anomalies
Some
irregularities
occur when there
are enough
electrons to halffill s and d
orbitals on a
given row.
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Electronic
Structure
of Atoms
Some Anomalies
For instance, the
electron
configuration for
copper is
[Ar] 4s1 3d5
rather than the
expected
[Ar] 4s2 3d4.
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Electronic
Structure
of Atoms
Some Anomalies
• This occurs
because the 4s
and 3d orbitals
are very close in
energy.
• These anomalies
occur in f-block
atoms, as well.
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Electronic
Structure
of Atoms
Example: What are the quantum numbers and
names (for example, 2s, 2p) of the orbitals in the
n = 4 principal level? How many orbitals exist?
Given: n = 4
Find: orbital designations, number of orbitals
Conceptual
ml
n
l
Plan:
0 → (n − 1)
Relationships:
Solve:
−l → +l
l: 0 → (n − 1); ml: −l → +l
n=4
 l : 0, 1, 2, 3
n = 4, l = 0 (s) n = 4, l = 1 (p)
n = 4, l = 2 (d)
n = 4, l = 3 (f)
ml : 0
ml : −1,0,+1 ml : −2,−1,0,+1,+2 ml : −3,−2,−1,0,+1,+2,+3
1 orbital
3 orbitals
5 orbitals
7 orbitals
4s
4p
4d
4f
total of 16 orbitals: 1 + 3 + 5 + 7 = 42 : n2
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