6/3/2012
1
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
Chapter 6
Electronic Structure
of Atoms
Chemistry, The Central Science, 11th edition
Theodore L. Brown; H. Eugene LeMay, Jr.;
and Bruce E. Bursten
John D. Bookstaver
St. Charles Community College
Cottleville, MO
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
Chapter 6 Problems
• Problems 13, 15, 21, 33, 35, 47, 51, 53,
63, 65, 67, 71, 73
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
Electronic Structure of Atoms
• To understand the electronic structure
of atoms, one must understand the
nature of electromagnetic radiation.
6/3/2012
2
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
Electromagnetic Radiation
• Electric and magnetic
fields propagate as waves
through empty space or
through a medium.
• A wave transmits energy.
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
Waves
• The distance between corresponding points
on adjacent waves is the wavelength ().
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
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.
6/3/2012
3
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
EM Radiation
Low
High
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
• Waves have a frequency • Use the Greek letter “nu”, , for frequency,
and units are “cycles per sec” • All radiation: • = c • c = velocity of light = 3.00 x 108 m/sec
• Long wavelength --> small frequency
• Short wavelength --> high frequency
= c/λ
Electromagnetic Radiation
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
Red light has = 700 nm. Calculate the
frequency. = c/λ
Freq = 3.00 x 108 m/s
7.00 x 10-7 m 4.29 x 1014 sec-1
700 nm • 1 x 10 -9 m
1 nm = 7.00 x 10 -7 m
Electromagnetic Radiation
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4
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
Electromagnetic Radiation
• All electromagnetic radiation travels at the same velocity: the speed of light (c),
3.00 108 m/s.
• Therefore,
c =
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
Electromagnetic Spectrum
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
Constructive and Destructive
Interference
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5
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
The Nature of Energy
• 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.
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
Black Body Radiation
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
Quantum Theory Blackbody Radiation:
Max Planck, 1900
є = h Energy, like matter, is discontinuous.
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6
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
Long wavelength -->
small frequency
low energy
Short wavelength -->
high frequency
high energy
Electromagnetic Radiation
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
Light with a short (large ) has a large E.
Light with large (small ) has a small E.
E = h •
Quantization of Energy
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
The Photoelectric Effect
• Heinrich Hertz, 1888
– Light striking the surface of certain metals causes ejection of electrons.
– > o
threshold frequency
I Albert Einstein 1905
6/3/2012
7
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
The Nature of Energy
• Einstein used Planck’s
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.
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
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 =
E = h
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
Sample Exercise 6.3 Energy of a Photon
Calculate the energy of one photon of yellow light with a wavelength of 589 nm.
We can use Equation 6.1 to convert the
wavelength to frequency:
We can then use Equation 6.3 to calculate
energy:
Solve: The frequency, v, is calculated from the
given wavelength.:
:
Use the frequency and Planck’s constant
to calculate the energy of the photon.
Comment: If one photon of radiant energy
supplies 3.37 × 10–19 J, then one mole
of these photons will supply
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8
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
The Nature of Energy
Another mystery in
the early 20th
century involved the
emission spectra
observed from
energy emitted by
atoms and
molecules.
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
9-2 Atomic Spectra
(a) (b) (c) (d) (e)
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
Atomic Spectra
Helium
Hydrogen
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9
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
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.
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
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).
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
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.
6/3/2012
10
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
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
E = h
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
8-4 The Bohr Atom
E = -RH
n2
RH = 2.179 10-18 J
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
Energy-Level Diagram
ΔE = Ef – Ei = -RH
nf2
-RH
ni2
–
= RH ( ni
2
1
nf2
– 1 ) = h = hc/λ
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Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
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
ni2
1
nf2
-
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.
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
Sample Exercise 6.4 Electronic Transitions in the Hydrogen Atom
Using Figure 6.14, predict which of the following electronic
transitions produces the spectral line having the longest
wavelength: n = 2 to n = 1, n = 3 to n = 2, or n = 4 to n = 3.
Solution
The longest wavelength will be associated with the lowest
frequency.
According to Planck’s equation, E = hv, the lowest frequency
is associated with the lowest energy.
In Figure 6.14 the shortest vertical line represents the smallest
energy change. Thus, the n = 4 to n = 3 transition produces the
longest wavelength (lowest frequency) line.
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
6/3/2012
12
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
Emission and Absorption Spectroscopy
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
Quantum Mechanical View of Electron
• Bohr’s Model only worked for a one-
electron atom.
• Scientists began to view the electron as
a wave.
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
Two Ideas Leading to a New
Quantum Mechanics
• Wave-Particle Duality
– Einstein suggested particle-like
properties of light could explain the
photoelectric effect.
– Diffraction patterns suggest photons
are wave-like.
• deBroglie, 1924
– Small particles of matter may at
times display wavelike properties. Louis de Broglie
Nobel Prize 1918
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13
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
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
mv
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
The Uncertainty Principle
• Heisenberg showed that the more precisely
the momentum of a particle is known, the less
precisely is its position known:
• In many cases, our uncertainty of the
whereabouts of an electron is greater than the
size of the atom itself!
(x) (mv) h
4
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
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.
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14
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
Quantum Mechanics
• The wave equation is
designated with a lower
case Greek psi ().
• 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.
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
Wave Functions
• ψ, psi, the wave function.
– Should correspond to a
standing wave within the
boundary of the system
being described.
• Particle in a box.
L
xnsin
L
2ψ
Slide 28 of 50 General Chemistry: Chapter 8 Prentice-Hall © 2007
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
Probability of Finding an Electron
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15
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
Wave Functions for Hydrogen
• Schrödinger, 1927 Eψ = H ψ
– H (x,y,z) or H (r,θ,φ)
ψ(r,θ,φ) = R(r) Y(θ,φ)
R(r) is the radial wave function.
Y(θ,φ) is the angular wave function.
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
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.
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
Principle Shells and Subshells • Principle electronic shell, n = 1, 2, 3…
• Angular momentum quantum number, l = 0, 1, 2…(n-1)
l = 0, s
l = 1, p
l = 2, d
l = 3, f
• Magnetic quantum number, ml= - l …-2, -1, 0,
1, 2…+l
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Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
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.
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
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
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
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
© 2009, Prentice-Hall, Inc.
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, etc.
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
Magnetic Quantum Number (ml)
• Orbitals with the same value of n form a shell.
• Different orbital types within a shell are
subshells.
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
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
© 2009, Prentice-Hall, Inc.
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 electron.
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
p Orbitals
• The value of l for p orbitals is 1.
• They have two lobes with a node between
them.
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
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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19
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
Energies of Orbitals
• For a one-electron
hydrogen atom,
orbitals on the same
energy level have
the same energy.
• That is, they are
degenerate.
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
Energies of Orbitals
• 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.
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
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.
6/3/2012
20
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
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.
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
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.
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
Electron Configurations
• This shows the
distribution of all
electrons in an atom.
• Each component
consists of
– A number denoting the
energy level,
6/3/2012
21
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
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,
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
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.
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
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
© 2009, Prentice-Hall, Inc.
Hund’s Rule
“For degenerate
orbitals, the lowest
energy is attained
when the number of
electrons with the
same spin is
maximized.”
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
Electron Configurations
• Aufbau process.
– Build up and minimize energy.
• Pauli exclusion principle.
– No two electrons can have all four
quantum numbers alike.
• Hund’s rule.
– Degenerate orbitals are occupied singly
first.
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
Orbital Filling
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Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
Aufbau Process and Hunds Rule
Electronic
Structure
of Atoms
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Filling p Orbitals
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
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.
6/3/2012
24
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
Some Anomalies
Some
irregularities
occur when there
are enough
electrons to half-
fill s and d
orbitals on a
given row.
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
Some Anomalies
For instance, the
electron
configuration for
chromium is
[Ar] 4s1 3d5
rather than the
expected
[Ar] 4s2 3d4.
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
Some Anomalies
For instance, the
electron
configuration for
copper is
[Ar] 4s1 3d10
rather than the
expected
[Ar] 4s2 3d9.
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25
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
Some Anomalies
• This occurs
because the 4s
and 3d orbitals
are very close in
energy.
• These anomalies
occur in f-block
atoms, as well.
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.
Filling the d Orbitals
Electronic
Structure
of Atoms
© 2009, Prentice-Hall, Inc.