Chapter 7 Atomic Structure and
the Periodic Table
The Trifid nebula, in the
constellation Sagittarius, is
5200 light years from Earth,
but we can study its
composition from the colors
of light emitted. The red color
arises from glowing hydrogen
atoms excited by hot young
stars at the center. The blue
glow nearby is light scattered
by dust clouds surrounding a
star that is not hot enough to
excite the surrounding
hydrogen atoms.
Assignment for Chapter 7
18, 27, 33, 43, 55, 65
Comte’s Agnosticism
(unknowablism)
“We will never know anything
about the stars because we
cannot get to them.”
Figure 7.1 (a) In a spectrometer, the light emitted by an
energetically excited sample of an element is passed through
a slit, to give a narrow ray, and then through a prism. The
prism separates the ray into different colors, which are
recorded photographically. The spectral lines on the
photograph are the separate images of the slit.
Spectroscopy is the most important tool for studying atomic
and molecular structure.
Figure 7.1 (b) A rainbow is formed when white light from the
Sun is split into its component colors by raindrops that act as
tiny prisms. The light enters the front of the raindrop, reflects
from the back, and emerges from the front. Double rainbows
are formed when the light reflects a second time inside the
drop.
Significant figure
Figure 7.2 The electric field of electromagnetic radiation
oscillates in space and time. The length of an arrow at any
point at a given instant represents the strength of the force
that the field exerts on a charged particle at that point. Note
the wavelike distribution of the field.
c   
c is a constant for all electromagnetic waves
Figure 7.3 The color of electromagnetic radiation is determined by its
wavelength (and frequency). (a) The wavelengths of the three rays
shown here are drawn to scale and you can see that the wavelengths
of green, yellow, and red light increase in that order. The perception
of color arises from the effect of the radiation on our eyes and the
response of our brain. (b) Each lamp in a traffic signal generates
white light, a mixture of all colors, but the tinted glass screens allow
only certain wavelengths to pass through.
(b)
Figure 7.4 This diagram represents a “snapshot” of an
electromagnetic wave at a given instant. The distance between
the peaks is the wavelength of the radiation. The amplitude
(height) of the peaks depends on the intensity of the radiation.
Figure 7.5 Wavelength and frequency are inversely related. The two
parts of this illustration show the electric field at three instants that
you might experience as a single wave flashed by a single point at
the speed of light from left to right. The position of the wave at the
first instant is the light gray wave and its position at the third instant
is the blue wave. (a) Short-wavelength radiation: note how the electric
field changes markedly at the three successive instants. (b) For the
same three instants, the electric field of the long-wavelength
radiation changes much less. Short-wavelength radiation has a high
frequency, whereas long-wavelength radiation has a low frequency.

c
Figure 7.6 The electromagnetic spectrum and the names of its
regions. Note that the region we call “visible light” occupies a
very narrow range of wavelengths. The regions are not shown
to scale.
Figure 7.7 When a metal is illuminated with light, electrons are
ejected, provided the frequency is above a threshold
frequency that is characteristic of the metal. Radiation with a
lower frequency will not cause electrons to be ejected, no
matter how intense it is.
Ee  I
Ee  
Wave theory of light cannot explain photoelectric effect!
Light must consist of photons (quantum of light).
Ee  
Figure 7.8 The red glow from this hydrogen discharge lamp
comes from excited hydrogen atoms that are returning to a
lower energy state and emitting the excess energy as visible
radiation.
E p  h  E
Figure 7.9 The spectrum of atomic hydrogen. The spectral
lines have been assigned to various groups of similar
wavelength called series; the Balmer and Lyman series are
shown here.
Each line corresponds to a photon emit by an electron
“jumping” from higher energy level to the ground state
Discrete spectral lines imply discrete structure of
electronic energy
Figure 7.10 When an atom undergoes a transition from a state
of higher energy to one of lower energy, it loses energy that is
carried away as a photon. The greater the energy loss, the
higher the frequency (and the shorter the wavelength) of the
radiation emitted. Thus, transition A generates light with a
higher frequency and shorter wavelength than transition B.
Figure 7.11 The spectrum of atomic hydrogen (reproduced on
the right) tells us the arrangement of the energy levels of the
atom because the frequency of the radiation emitted in a
transition is proportional to the energy difference between the
two energy levels involved. The 0 on the energy scale
corresponds to the completely separated proton and electron.
The numbers on the right label the energy levels: they are
examples of quantum numbers (see Section 7.7).
Signature of Atoms
 H  RH ( n1  n1 )
2
1
2
2
n1  1,2,3,    ; n2  n1  1, n1  2,    
Figure 7.12 When a guitar string vibrates, only certain
wavelengths can be sustained over time—those for which the
amplitude of the wave goes to 0 at each end. One or more
complete half-wavelengths must fit exactly between the end
points. (a) A guitar string at rest. (b) One-half wavelength. (c)
One full wavelength.
Wave-Particle Duality
All particles show wavelike properties
All waves have particle behaviors

h
mv
An electron t raveling at 2.2 106 m/s :

6.6271034 Js
9.1091031 kg 2.2106 m / s
 3.3 10
10
m
Figure 7.13 Davisson and Germer showed that electrons give a
diffraction pattern when reflected from a crystal. G. P.
Thomson working in Aberdeen, Scotland showed that they
also give a diffraction pattern when they pass through a very
thin gold foil. The latter is shown here. G. P. Thomson was the
son of J. J. Thomson, who identified the electron (Section 1.3).
Both received Nobel prizes, J. J. for showing that the electron
is a particle and G. P. for showing that it is a wave.
Figure 7.14 (a) In classical mechanics, a particle follows a
path, or trajectory, and its position can be predicted at any
instant. (b) In quantum mechanics, the particle is distributed
like a wave, so its location cannot be predicted exactly. Where
the wavefunction has a high amplitude, there is a high
probability of finding the particle; where the amplitude is low,
there is only a small probability of finding the particle.
Figure 7.15 Erwin Schrödinger (1887–1961). The Schrödinger
equation is shown superimposed on Schrödinger’s head. The
constant stands for h /2.
 2
 2m ( x 2 
 2
y 2

 2
z 2
)  V  E
Erwin Schrödinger, 1000 Austrian Schilling (1983)
Electrons are waves inside an atom.
…..not particles.
They don’t believe me…I quit!
Figure 7.16 The Born interpretation of a wavefunction. The
probability of the electron being found at a point is
proportional to the square of the wavefunction (indicated by
2), as depicted by the density of shading in the band below.
Note that the probability density is 0 at a node. A node is a
point where the wavefunction passes through 0, not merely
approaches 0.
Wave = wave of probability
Figure 7.17 The three-dimensional electron cloud
corresponding to an electron in the lowest energy state of
hydrogen. This wavefunction is called the 1s-orbital (Section
7.7). The density of shading represents the probability of
finding the electron at any point. The superimposed graph
shows how the probability varies with the distance from the
nucleus along any radius.
Cloud = cloud of probability
Figure 7.18 The simplest way of drawing an atomic orbital is
as a boundary surface, a surface within which there is a high
probability (typically, 90%) of finding the electron. The spheres
here represent the boundary surfaces of the s-orbitals in the
first three energy levels. Note that s-orbitals with n > 1 have
internal spherical nodes and that the size of the orbital
increases with n. We shall use blue to denote s-orbitals, but
that color is only an aid to their identification.
These s-orbitals are waves.
 H  RH ( n1  n1 )
2
1
2
2
n1  1,2,3,    ; n2  n1  1, n1  2,    
Figure 7.19 The boundary surface of a p-orbital has two lobes;
the nucleus lies on the plane that divides the two lobes, and
an electron will, in fact, never be found at the nucleus itself if it
is in a p-orbital. There are three p-orbitals of a given energy,
and they lie along three perpendicular axes. We shall use
yellow to indicate p-orbitals. Note that the orbital has opposite
signs (as depicted by the depth of color) on each side of the
nodal plane.
These p-orbitals are waves.
Figure 7.20 The boundary surface of a d-orbital is more
complicated than that of an s- or a p-orbital. There are five dorbitals of a given energy; four of them have four lobes; one is
slightly different. In each case, an electron that occupies a dorbital will not be found at the nucleus. We shall use orange to
indicate d-orbitals, with different depths of color to indicate
different signs.
These d-orbitals are waves.
Figure 7.21 The boundary surface of one of the seven forbitals of a shell (with n  4). The f-orbitals have a complex
appearance. Their shapes will not be needed again in this text.
However, their existence is important for understanding the
periodic table, the presence of the lanthanides and actinides,
and the properties of the later d-block elements.
This f-orbital is a wave.
All f-orbitals
These f-orbitals are waves.
Figure 7.22 The permitted energy levels of a hydrogen atom
as calculated from Eq. 6. The 0 on the energy scale
corresponds to the completely separated proton and electron;
the lowest energy state lies at hR H below the 0 of energy. The
levels are labeled with the principal quantum number, n, which
ranges from 1 (for the lowest state) to infinity (for the
separated proton and electron). Compare this diagram with the
experimentally determined array of levels shown in Fig. 7.11.
Figure 7.23 A summary of the arrangement of shells, subshells, and
orbitals in an atom and the corresponding quantum numbers. Note
that the quantum number ml is an alternative label for the individual
orbitals: in chemistry, it is more common to use x, y, and z as labels,
as shown in Figs. 7.19 and 7.20. There is no direct correspondence
between axis designation and the numerical value of ml.
Figure 7.24 The solution to Example 7.5. The boxes represent
the individual orbitals in each subshell. There are 16 orbitals in
the shell with n  4, each of which can hold two electrons.
The atomic orbitals for n=4
Investigating Matter 7.1 The quantization of electron spin is
confirmed by the Stern-Gerlach experiment, in which a stream
of atoms splits into two as it passes between the poles of a
magnet. The atoms in one stream have an odd  electron, and
those in the other an odd  electron.
Figure 7.25 The two spin states of an electron can be
represented as clockwise or counterclockwise rotation around
an axis passing through the electron. The two states are
labeled by the quantum number ms and depicted by the arrows
shown on the right.
7.9 The Electronic Structure of Hydrogen
Free electron state
3p 3,1,1,1/2 3,1,1,-1/2 3,1,0,1/2 3,1,0,-1/2 3,1,-1,1/2 3,1,-1,-1/2
3s 3,0,0,1/2 3,0,0,-1/2
2p 2,1,1,1/2 2,1,1,-1/2 2,1,0,1/2 2,1,0,-1/2 2,1,-1,1/2 2,1,-1,-1/2
2s 2,0,0,1/2 2,1,1,-1/2
1s 1,0,0,1/2 1,0,0,-1/2
Ionization energy=hRH=2x10-18J
Lithium
Sodium
Potassium
Rubidium
Fingerprint or Signature or ID of
Atoms (Molecules)
What can we learn
from these scenes?
The Building-up Principle
Pauli’s Exclusion Principle:
No more than two electrons may occupy
any given orbital. When two electrons do
occupy one orbital, their spins must be
paired.
Hund’s Rule:
If more than one orbital in a subshell is
available, electrons will fill empty orbitals
before pairing on one of them.
Ground state (configuration)
An Example Sulfur (Z=16)
4f
4d
4p
4s
3d
3p
3s
2p
2s
1s
Another Example O2-(Z=8)
3d
3p
3s
2p
2s
1s
Electron-Electron Interactions
Consequences of Electron-Electron Interactions
Orbital energy:
Electron-Nucleuspull (attractive)
Electron-Electronpush(repulsive)
Shielding: The attraction is reduced
because of the presence of other
electrons Zeff < Z
Z
Z
Zeff = Z-S
Z
Penetration: s-electrons get very close
to the nucleus, reducing their energy
The “trajectories” of s-electrons
(penetration)
Orbital Energy Crossing
For atoms with Z>20, energy
crossing (typically a 4s-electron has
lower energy than a 3d electron—
against the building-up principle)
occurs because shielding increases
the energy of non-s-electrons in
outer shells whereas penetration
reduces the energy of s-electrons.
Periodical Table
Dmitri Ivanovich Mendeleev
(1834-1907)
Other Periodical Properties
•
•
•
•
•
•
Effective nuclear charge
Atomic radius
Ionic radius
Ionization energy
Electron affinity
……
Effective Nuclear Charge
Atomic Radius
2r
The outmost electrons in metals experience little
attraction from the nucleus and can spread in a
large space-hence large atomic radius.
The case is opposite in nonmetal atoms.
Atomic Radius
Ionic Radius
Notice the difference between ionic radius and atomic radius.
Atomic Radius and Ionic Radius
Notice the difference between anions and cations
(First) Ionization Energy
1
A  A  e H
(1)
 first ionization energy
A1  A2  e H (2)  second ionization energy
H (2)
H (1)
A  A1  e H (1)  first ionization energy
A1  A2  e H (2)  second ionization energy
H (2)
H (1)
Electron Affinity

A  e 
A
H  electron affinity
A  e 
 A
-
-
--
H  electron affinity
Electron Affinity and Electronegativity
Periodical Properties of Atoms
Group 1
Group 14
Silicon
Carbon
Tin
Germanium
Lead
Group 16
Oxygen
Sulfur
Selenium
Tellurium
Diagonal Relationship
In addition to horizontal and vertical trends, there is a diagonal relationship
between elements such as Li and Mg, Be and Al, B and Si, that have an adjacent
upper left/lower right relative location in the periodic table.
These pairs of elements have similar size and electronegativity, resulting in
similar properties.
Born (top) and silicon (bottom)
Why diagonal relationship?
Size decreases moving left to right across a row and
increases moving right to left
Size decreases moving up a period and increases moving down
First row of d block
Scandium Titanium Vanadium Chromium Manganese
Iron
Cobalt
Nickel
Copper
Zinc
雙點擊下表，然後點選執行，在點
選任一元素，即可得知其主要性質
。
Assignment for Chapter 7
18, 27, 33, 43, 55, 65