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Chapter 5
Periodicity and the Electronic Structure of Atoms
國防醫學院 生化學科
王明芳老師
2011-10-4
1
2
Light and the Electromagnetic
Spectrum
Electromagnetic energy (―light‖) is characterized by
wavelength, frequency, and amplitude.
Chapter 5/3
Light and the Electromagnetic
Spectrum
Chapter 5/4
Light and the Electromagnetic
Spectrum

l
Chapter 5/5
Light and the Electromagnetic
Spectrum
Wavelength x Frequency = Speed
l
m
x

1
s
=
c
m
s
hertz (Hz; 1 Hz = 1s-1)
c is defined to be the rate of travel of all electromagnetic
energy in a vacuum and is a constant value—speed of
m
light.
8
c = 3.00 x 10 s
Chapter 5/6
Light and the Electromagnetic
Spectrum
The light blue glow given off by mercury streetlamps
has a frequency of 6.88 x 1014 s-1 (or, Hz). What is the
wavelength in nanometers?
l= c =

m
8
3.00 x 10 s
6.88 x
1 x 109 nm
m
1014
1
s
= 436 nm
Chapter 5/7
Example 5.1 Calculating A Frequency From A Wavelength
The light blue glow given off by mercury streetlamps has a wavelength of 436 nm. What
is its frequency in hertz?
Solution
Don’t forget to convert from nanometers to meters.
Electromagnetic Energy and
Atomic Line Spectra
Glass prism
sundog
Chapter 5/9
Electromagnetic Energy and
Atomic Line Spectra
Line Spectrum: A series of discrete lines on an
otherwise dark background as a result of light emitted
by an excited atom
Atomic line spectra
Chapter 5/10
Electromagnetic Energy and
Atomic Line Spectra
Johann Balmer in 1885 discovered a mathematical
relationship for the four visible lines in the atomic line
spectra for hydrogen.
1
1
1
m = 2 visible light
=R
22 n2
l
Johannes Rydberg later modified the equation to fit
every line in the entire spectrum of hydrogen.
1
1
1
=R
m2 n2
l
m=1
m=3
UV light
infrared light
R (Rydberg Constant) = 1.097 x 10-2 nm-1
Chapter 5/11
Example 5.2 Using The Balmer–Rydberg Equation
What are the two longest-wavelength lines in nanometers in the series of the
hydrogen spectrum when
m = 1 and n > 1?
Solution
The wavelength l is greatest when n is smallest; that is, when
n = 2 and n = 3.
Solving the equation first for n = 2 gives
Example 5.2 Using The Balmer–Rydberg Equation
Continued
The two longest-wavelength lines are at 121.5 nm and
102.6 nm.
Example 5.3 Using The Balmer–Rydberg Equation
What is the shortest-wavelength line in nanometers in the series
of the hydrogen spectrum when m = 1 and n > 1?
Solution
The shortest-wavelength line occurs when is infinitely
large so that 1/n2 is zero. That is, if n = , then 1/n2 =
0.
Solution
The shortest-wavelength line is at 91.16 nm.
Particlelike Properties of
Electromagnetic Energy
Photoelectric Effect:
Irradiation of clean metal
surface with light causes
electrons to be ejected from
the metal. Furthermore, the
frequency of the light used
for the irradiation must be
above some threshold value,
which is different for every
metal.
A glass window can be broken by
a single baseball, but a thousand
Ping-Pong ball would only bounce
off.
Chapter 5/15
Particlelike Properties of
Electromagnetic Energy
The photoelectric effect: the energy of an individual photo depends only on
its frequency (or wavelength), not on the intensity of the light beam.
The intensity of a light beam is a measure of the number of photo in the beam.
Chapter 5/16
Particlelike Properties of
Electromagnetic Energy
E = h
E

h (Planck’s constant) = 6.626 x 10-34 J s
Electromagnetic energy (light) is quantized.
Chapter 5/17
Particlelike Properties of
Electromagnetic Energy
Niels Bohr proposed in 1914 a model of the
hydrogen atom as a nucleus with an electron circling
around it.
In this model, the energy levels of the orbits are
quantized so that only certain specific orbits
corresponding to certain specific energies for the
electron are available.
Chapter 5/18
Particlelike Properties of
Electromagnetic Energy
Chapter 5/19
Example 5.4 Calculating the Energy of a Photon
from its Frequency
What is the energy in kilojoules per mole of radar waves with 
= 3.35  108 Hz?
Strategy
1. E = h
2. To find the energy per mole of photons, the energy of one
photon must be multiplied by Avogadro’s number.
Solution
Wavelike Properties of Matter
Louis de Broglie in 1924 suggested that, if light can
behave in some respects like matter, then perhaps
matter can behave in some respects like light.
In other words, perhaps matter is wavelike as well as
particlelike.
h
l=
mv
The de Broglie equation allows the calculation of a
―wavelength‖ of an electron or of any particle or
object of mass m and velocity v.
Chapter 5/21
Wavelike Properties of Matter
What is the de Broglie wavelength in meters of a
small car with a mass of 1150 kg traveling at a
velocity of 24.6 m/s?
l= h =
mv
2
kg
m
6.626 x 10-34 s
m
(1150 kg) 24.6 s
= 2.34 x 10-38 m
Chapter 5/22
Quantum Mechanics and the
Heisenberg Uncertainty Principle
In 1926 Erwin Schrödinger proposed the quantum
mechanical model of the atom which focuses on the
wavelike properties of the electron.
In 1927 Werner Heisenberg stated that it is
impossible to know precisely where an electron is
and what path it follows—a statement called the
Heisenberg uncertainty principle.
Chapter 5/23
Wave Functions and Quantum
Numbers
Wave solve Wave function
equation
or orbital (Y )
Probability of finding
electron in a region
of space (Y 2)
A wave function is characterized by three
parameters called quantum numbers, n, l, ml.
Chapter 5/24
Wave Functions and Quantum
Numbers
Principal Quantum Number (n)
• Describes the size and energy level of the orbital
•
Commonly called a shell
•
Positive integer (n = 1, 2, 3, 4, …)
•
As the value of n increases:
•
The energy increases
•
The average distance of the e- from the
nucleus increases
Chapter 5/25
Wave Functions and Quantum
Numbers
Angular-Momentum Quantum Number (l)
• Defines the three-dimensional shape of the orbital
• Commonly called a subshell
• There are n different shapes for orbitals
• If n = 1 then l = 0
• If n = 2 then l = 0 or 1
• If n = 3 then l = 0, 1, or 2
• Commonly referred to by letter (subshell notation)
• l=0
s (sharp)
• l=1
p (principal)
• l=2
d (diffuse)
• l=3
f (fundamental)
Chapter 5/26
Wave Functions and Quantum
Numbers
Magnetic Quantum Number (ml )
• Defines the spatial orientation of the orbital
•
There are 2l + 1 values of ml and they can
have any integral value from -l to +l
•
If l = 0 then ml = 0
•
If l = 1 then ml = -1, 0, or 1
•
If l = 2 then ml = -2, -1, 0, 1, or 2
•
etc.
Chapter 5/27
Wave Functions and Quantum
Numbers
Chapter 5/28
Wave Functions and Quantum
Numbers
Chapter 5/29
Wave Functions and Quantum
Numbers
Identify the possible values for each of the three
quantum numbers for a 4p orbital.
Chapter 5/30
Wave Functions and Quantum
Numbers
Identify the possible values for each of the three
quantum numbers for a 4p orbital.
n=4
l=1
ml = -1, 0, or 1
Chapter 5/31
Example 5.5 Using Quantum Numbers To Identify
An Orbital
Identify the shell and subshell of an orbital with the
quantum numbers n = 3, l = 1, ml = 1.
Solution
1. The principal quantum number gives the shell number
2. The angular-momentum quantum number gives the subshell
designation.
3. The magnetic quantum number ml is related to the spatial
orientation of the orbital.
A value of n = 3 indicates that the orbital is in the third shell,
and a value of l = 1 indicates that the orbital is of
the p type. Thus, the orbital has the designation 3p.
Example 5.6 Assigning Quantum Numbers To An
Orbital
Give the possible combinations of quantum numbers for a 4p
orbital.
Solution
The designation 4p indicates that the orbital has a principal
quantum number n = 4 and an angular-momentum quantum
number l = 1. The magnetic quantum number ml can have
any of the three values 1, 0, or +1.
The allowable combinations are
n = 4, l = 1, ml = 1
n = 4, l = 1, ml = 0
n = 4, l = 1, ml = +1
The Shapes of Orbitals
Node: A surface of
zero probability for
finding the electron
Representations of 1s, 2s, and 3s orbitals
Chapter 5/34
The Shapes of Orbitals
s Orbital Shapes:
1. All s orbitals are spherical; The probability of
finding an s electron depends only on distance
from the nucleus, not on direction.
2. Only one orientation of a sphere in space, ml = 0
3. Only one s orbital per shell.
4. The size of the s orbital is successively higher
shells an electron in an outer-shell s orbital is
farther from the nucleus on average than and
electron in an inner-shell s orbital.
Chapter 5/35
The Shapes of Orbitals
Node: A surface of
zero probability for
finding the electron
Chapter 5/36
The Shapes of Orbitals
Representations of the three 2p orbitals
Chapter 5/37
The Shapes of Orbitals
p Orbital Shapes:
1. The p orbitals are dumbbell-shaped, with their
electron distribution concentrated in identical
lobes on either side of the nucleus and
separated by a nodal plane passing through the
nucleus.
2. These two lobes have different phases. Only
lobes of the same phase can interact in forming
covalent chemical bonds.
Chapter 5/38
Representations of the five 3d orbitals (a-d)
Also shown is one of the seven 4f orbital (f)
The Shapes of Orbitals
d and f Orbital Shapes:
1. Four d orbitals are cloverleaf-shaped, with four
lobes separated by two nodal planes through the
nucleus; one is similar in shape to a pz but with a
donut-shaped region of electron probability.
2. Both the number of nodal planes and the
geometric complexity of the orbitals increases with
the quantum number increases of the subshell.
Chapter 5/40
Quantum Mechanics and
Atomic Line Spectra
The origin of atomic line spectra.
The energies available to electrons are quantized and can have only the
specific values associated with the orbitals they occupy.
Chapter 5/41
Quantum Mechanics and
Atomic Line Spectra
m: shell the transition
is to (inner-shell)
1
1
1
=R
2
m
n2
l
n: shell the transition
is from (outer-shell)
Chapter 5/42
Example 5.7 Calculating The Energy Difference Between Two Orbitals
What is the energy difference in kilojoules per mole between the first and second
shells of the hydrogen atom if the lowest-energy emission in the spectral series
with m = 1 and n = 2 occurs at l = 121.5 nm?
Solution
1. The lowest-energy emission line in the spectral series with m = 1 and n = 2
corresponds to the emission of light as an electron falls from the second shell to
the first shell
2. The energy of that light equal to the energy difference between shells.
3. Knowing the wavelength of the light, we can calculate the energy of one photon
using the equation, E = hc/l , and then multiply by Avogadro’s number to find
the answer in joules (or kilojoules) per mole:
The energy difference between the first and second shells of the hydrogen atom is 985 kJ/mol.
Electron Spin and the Pauli
Exclusion Principle
Electrons have spin which gives rise to a tiny magnetic
field and to a spin quantum number (ms).
Spin quantum number (ms) can have
either of two values, +1/2 or -1/2.
The value of ms is independent of the
other three quantum number, unlike
the values of n, l, and ml, which are
interrelated
Electron spin
Pauli Exclusion Principle: No two electrons in an
atom can have the same four quantum numbers.
Chapter 5/44
Orbital Energy Levels in
Multielectron Atoms
Effective Nuclear Charge (Zeff): The nuclear
charge actually felt by an electron
Zeff = Zactual - Electron shielding
Effective Nuclear Charge, Zeff
1. The energy split between subshells is comes from the
balance of attractions and repulsions in the atom.
2. Shielding effect: Each electrons is shielded from the
full attraction of the nucleus by the other electrons in
the atom.
3. Electron shielding leads to energy differences among
orbitals within a shell.
Chapter 5/46
Effective Nuclear Charge, Zeff
4. Net nuclear charge felt by an electron is called the
effective nuclear charge (Zeff).
5. Zeff is lower than actual nuclear charge.
6. Electrons in different orbitals are shielded differently
and feel different values of Zeff.
7. This explains certain periodic changes observed.
Chapter 5/47
Orbital Energy Levels in
Multielectron Atoms
Effective Nuclear Charge (Zeff): The nuclear
charge actually felt by an electron
Zeff = Zactual - Electron shielding
Chapter 5/48
Electron Configurations of
Multielectron Atoms
Electron Configuration: A description of which
orbitals are occupied by electrons
Degenerate Orbitals: Orbitals that have the
same energy level. For example, the three p
orbitals in a given subshell
Ground-State Electron Configuration: The
lowest-energy configuration
Aufbau Principle (“building up”): A guide for
determining the filling order of orbitals
Chapter 5/49
Electron Configurations of
Multielectron Atoms
Rules of the aufbau principle:
1. Lower-energy orbitals fill before higher-energy orbitals.
2. An orbital can only hold two electrons, which must
have opposite spins (Pauli exclusion principle).
3. If two or more degenerate orbitals are available, follow
Hund’s rule.
Hund’s Rule: If two or more orbitals with the same energy
are available, one electron goes into each until all are halffull. The electrons in the half-filled orbitals all have the
same value of their spin quantum number.
Chapter 5/50
Electron Configurations of
Multielectron Atoms
Chapter 5/51
Electron Configuration of
Multielectron Atoms
Increasing Energy
Core
[He]
[Ne]
[Ar]
[Kr]
[Xe]
[Rn]
1s
2s
3s
4s
5s
6s
7s
2p
3p
4p
5p
6p
7p
3d
4d 4f
5d 5f
6d
Chapter 5/52
Electron Configurations of
Multielectron Atoms
Electron
Configuration
H:
1s1
1 electron
s orbital (l = 0)
n=1
Chapter 5/53
Electron Configurations of
Multielectron Atoms
Electron
Configuration
H:
1s1
He:
1s2
2 electrons
s orbital (l = 0)
n=1
Chapter 5/54
Electron Configurations of
Multielectron Atoms
Electron
Configuration
H:
He:
Li:
1s1
1s2
Lowest energy to highest energy
1s2 2s1
1 electron
s orbital (l = 0)
n=2
Chapter 5/55
Electron Configurations of
Multielectron Atoms
Electron
Configuration
H:
1s1
He:
1s2
Li:
1s2 2s1
N:
1s2 2s2 2p3
3 electrons
p orbital (l = 1)
n=2
Chapter 5/56
Electron Configurations of
Multielectron Atoms
Electron
Configuration
H:
Orbital-Filling
Diagram
1s1
1s
He:
1s2
Li:
1s2 2s1
N:
1s2 2s2 2p3
Chapter 5/57
Electron Configurations of
Multielectron Atoms
Electron
Configuration
H:
Orbital-Filling
Diagram
1s1
1s
He:
1s2
Li:
1s2 2s1
N:
1s2 2s2 2p3
1s
Chapter 5/58
Electron Configurations of
Multielectron Atoms
Electron
Configuration
H:
Orbital-Filling
Diagram
1s1
1s
He:
1s2
Li:
1s2 2s1
N:
1s2 2s2 2p3
1s
1s 2s
Chapter 5/59
Electron Configurations of
Multielectron Atoms
Electron
Configuration
H:
Orbital-Filling
Diagram
1s1
1s
He:
1s2
Li:
1s2 2s1
N:
1s2 2s2 2p3
1s
1s 2s
1s 2s
2p
Chapter 5/60
Electron Configurations of
Multielectron Atoms
Electron
Configuration
Na:
P:
1s2 2s2 2p6 3s1
Shorthand
Configuration
[Ne] 3s1
1s2 2s2 2p6 3s2 3p3
Ne configuration
Chapter 5/61
Electron Configurations of
Multielectron Atoms
Electron
Configuration
Na:
Shorthand
Configuration
1s2 2s2 2p6 3s1
Ne configuration
Chapter 5/62
Electron Configurations of
Multielectron Atoms
Electron
Configuration
Na:
1s2 2s2 2p6 3s1
Shorthand
Configuration
[Ne] 3s1
Ne configuration
Chapter 5/63
Electron Configurations of
Multielectron Atoms
Electron
Configuration
Na:
P:
Shorthand
Configuration
1s2 2s2 2p6 3s1
[Ne] 3s1
1s2 2s2 2p6 3s2 3p3
[Ne] 3s2 3p3
Ne configuration
Chapter 5/64
Electron Configurations of
Multielectron Atoms
Electron
Configuration
Shorthand
Configuration
1s2 2s2 2p6 3s1
[Ne] 3s1
P:
1s2 2s2 2p6 3s2 3p3
[Ne] 3s2 3p3
K:
1s2 2s2 2p6 3s2 3p6 4s1
[Ar] 4s1
1s2 2s2 2p6 3s2 3p6 4s2 3d1
[Ar] 4s2 3d1
Na:
Sc:
Ar configuration
Chapter 5/65
Electron Configurations of
Multielectron Atoms
Electron
Configuration
Shorthand
Configuration
1s2 2s2 2p6 3s1
[Ne] 3s1
P:
1s2 2s2 2p6 3s2 3p3
[Ne] 3s2 3p3
K:
1s2 2s2 2p6 3s2 3p6 4s1
Na:
Ar configuration
Chapter 5/66
Electron Configurations of
Multielectron Atoms
Electron
Configuration
Shorthand
Configuration
1s2 2s2 2p6 3s1
[Ne] 3s1
P:
1s2 2s2 2p6 3s2 3p3
[Ne] 3s2 3p3
K:
1s2 2s2 2p6 3s2 3p6 4s1
[Ar] 4s1
Na:
Ar configuration
Chapter 5/67
Electron Configurations of
Multielectron Atoms
Electron
Configuration
Shorthand
Configuration
1s2 2s2 2p6 3s1
[Ne] 3s1
P:
1s2 2s2 2p6 3s2 3p3
[Ne] 3s2 3p3
K:
1s2 2s2 2p6 3s2 3p6 4s1
[Ar] 4s1
Na:
Sc:
1s2 2s2 2p6 3s2 3p6 4s2 3d1
[Ar] 4s2 3d1
Ar configuration
Chapter 5/68
Some Anomalous Electron
Configurations
Expected
Configuration
Actual
Configuration
Cr:
[Ar] 4s2 3d4
[Ar] 4s1 3d5
Cu:
[Ar] 4s2 3d9
[Ar] 4s1 3d10
Chapter 5/69
Outer-shell, ground-stead electron configuration of
the elements
Electron Configurations and
the Periodic Table
Blocks of the
periodic table
Electron Configuration of
Multielectron Atoms
Increasing Energy
Core
[He]
[Ne]
[Ar]
[Kr]
[Xe]
[Rn]
1s
2s
3s
4s
5s
6s
7s
2p
3p
4p
5p
6p
7p
3d
4d 4f
5d 5f
6d
Chapter 5/72
Electron Configurations and
the Periodic Table
Valence Shell: Outermost shell.
Li: 2s1
Na: 3s1
Cl: 3s2 3p5
Br: 4s2 4p5
Chapter 5/73
Example 5.8 Assigning A Ground-State Electron Configuration To An Atom
Give the ground-state electron configuration of arsenic, Z = 33, and draw an orbital-filling diagram, indicating the
electrons as up or down arrows.
Solution
1.
2.
3.
Start with hydrogen at the upper left
Fill orbitals until 33 electrons have been added.
Remember that only 2 electrons can go into an orbital and that each one of a set of degenerate orbitals
must be half filled before any one can be completely filled.
As: 1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p3
or
[Ar] 4s2 3d10 4p3
An orbital-filling diagram indicates the electrons in each orbital
as arrows. Note that the three 4p electrons all have the same spin:
Example 5.9 Identifying An Atom From Its Ground-State Electron Configuration
Identify the atom with the following ground-state electron configuration:
Solution
1.
2.
One way to do this problem is to identify the electron configuration and decide which atom has that
configuration.
Alternatively, you can just count the electrons, thereby finding the atomic number of the atom.
The atom whose ground-state electron configuration is depicted is in the fifth row because it follows krypton. It
has the configuration 5s2 4d5, which identifies it as technetium. Alternatively, it has 36 + 7 = 43 electrons and is
the element with Z = 43.
Electron Configurations and
Periodic Properties: Atomic Radii
column
radius
row
radius
Atomic radii of the elements in picometers
Chapter 5/76
Electron Configurations and
Periodic Properties: Atomic Radii
Plots of atomic radius and calculated Zeff for the highestenergy electron versus atomic number
Chapter 5/77