p274

Chapter seven:

Atomic Structure and

Periodicity
Contents p274

2
 p275
7-1 Electromagnetic Radiation

Wave length

Frequency
 p276

The Nature
of Waves

4
Figure 7.1
Ex 7.1 Frequency of Electromagnetic Radiation P277

The brilliant red colors seen in fireworks are due to the

emission of light with wavelengths around 650 nm when
strontium salts such as Sr(NO3)2 and SrCO3 are heated. (This
can be easily demonstrated in the lab by dissolving ones of
these salts in methanol that contains a little water and igniting
the mixture in an evaporating dish.) Calculate the frequency
of red light of wavelength 6.50 × 102 nm.
Solution:
 Classification of p276

electromagnetic radiation

Figure 7.2

6
Flame Tests

7
Electromagnetic Waves

8
7-2 The Nature of Matter p277

s constant: 6.626 x 10-34 J‧ s

Planck’

where n is an integer (1, 2, 3….), ν is the

frequency of the electromagnetic radiation
absorbed or emitted.

Einstein suggested that electromagnetic radiation can be

viewed as a stream of “
particles”called photons.

9
Ex 7.2 The Energy of a Photon P278

The blue color in fireworks is often achieved by heating

copper(I) chloride (CuCl) to about 1200℃. Then the
compound emits blue light having a wavelength of 450 nm.
What is the increment of energy (the quantum) that is emitted
at 4.50 × 102 nm by CuCl?
Solution:
 The Photoelectric Effect p279

1. Studies in which the frequency of the light is varied show

that no electrons are emitted by a given metal below a
specific threshold frequency ν0.

2. For light with frequency lower than the threshold

frequency, no electrons are emitted regardless of the
intensity of the light.
 The Photoelectric Effect
3. For light with frequency greater than the
threshold frequency, the number of
electrons emitted increases with the
intensity of the light.

4. For light with frequency greater than the

threshold frequency, the kinetic energy, of
the emitted electrons increases linearly with
the frequency o the light.
12
The Photoelectric Effect

13
Ex 7.3 Calculations of Wavelength P281

Compare the wavelength for an electron (mass = 9.11 ×

10-31 kg) traveling at a speed of 1.0 × 107 m/s with that for
a ball (mass = 0.10 kg) traveling at 35 m/s.
Solution:
Pickle Light

15
7-3 The Atomic Structure
of Hydrogen
p284

Figure 7.6 (a) A continuous spectrum containing all wavelengths of

visible light (indicated by the initial letters of the colors of the
rainbow). (b) the hydrogen line spectrum contains only a few discrete
wavelength.
Emits a photon of light p285

Figure 7.7
A change between two discrete energy levels
emits a photon of light. 17
The Line Spectrum of Hydrogen

18
7-4 The Bohr Model p285

a. In 1013, a Danish physicist named Niels Bohr (1885-1962),

aware o the experimental results we have just discussed,
developed a quantum model for the hydrogen atom.

b. Bohr proposed that the electron in hydrogen atom moves

around the nucleus only in certain allowed circular orbits.

c. He calculated the radii for these allowed orbits by using the

theories of classical physics and by making some new
assumptions.
19
 Electronic Transitions in the Bohr Model for p285
the Hydrogen Atom

Line spectrum

Wavelength
Figure 7.8
Electronic transitions in the Bohr model for the hydrogen atom. (a)
An energy-level diagram for electronic transitions. (b) an orbit-
transition diagram, which accounts for the experimental spectrum.
(Note that the orbits shown are schematic. They are not drawn to
scale.) (c) The resulting line spectrum on a photographic plate. Note
that the lines in the visible region of the spectrum correspond to
transitions from higher levels to the n = 2 level. 20
 p285
Electronic Transitions in the Bohr
Model for the Hydrogen Atom

21
The most important equation to come from Bohr’ s model
is the expression for the energy levels available to the p286
electron in the hydrogen atom.

(7.1)

22
Ex 7.4 Energy Quantization in P287
Hydrogen
Calculate the energy requires to excite the hydrogen electron
from level n = 1 level to level n = 2. Also calculate the
wavelength of light that must be absorbed by a hydrogen
atom in its ground state to reach this excited state.
Solution:
 p288
A typical aerial shell used in fireworks displays. Time-
delayed fuses cause a shell to explode in stages. In
this case a red starburst occurs first, followed by a
blue starburst, and finally a flash and loud report.

24
 p289

fireworks

25
 P290
Ex 7.5 Electron Energies
Calculate the energy required to remove the
electron from a hydrogen atom in its ground state.
Solution
7-5 The Quantum Mechanical p290

Model of the Atom

Figure 7.9

27
 Quantum Mechanical Model p291

Wave function: is a function of coordinates (x, y, and z)

electron’
s position in three-dimensional space and H
represents a set of mathematical instruction’
s called an
operator.

In this case, the operator contained mathematical terms that

produce the total energy of the atom (the sum of the
potential energy due to the attraction between the proton
and electron and the kinetic energy of the moving electron).
28
Quantum Mechanical Model

When this equation is analyzed, many solutions are

found. Each solution consists of a wave function ψ
that is characterized by a particular value of E.

A specific wave function is often called an

orbital.

29
 p291
Quantum (wave) mechanical model

A orbital is not a Bohr orbit.

The wave function gives us no information about

the detailed pathway of the electron.

When we solve problems involving the motions of

particles in macroscopic world, we are able to
predict their pathways.
30
Heisenberg uncertainty principle p291

There is a fundamental limitation to just how

we can know both the position and
momentum of a particle at a given time.

Stated mathematically, the uncertainty

principle is

Δx ． Δ (m v) ≧ h /(4π)

31
 p292
The physical meaning of a Wave Function
The square of the wave function is most conveniently
represented as a probability distribution , in which the
intensity of color is used to indicate the probability value
near a given point on space.

 The probability distribution for the hydrogen 1s wave

function (orbital) is shown in Fig. 7.11(a).

32
 p292
The physical meaning of a Wave Function

The more times the electrons visits a particular point,

the darker the negative becomes.

This diagram is also known as an electron density

map; electron density and electron probability mean
the same thing.

33
When the total probability of finding the electron p292

in each spherical shell id plotted versus the

distance from the nucleus, the plot in Fig. 7.12(b)
is obtained.

This graph is called the radial

probability distribution. (a)

Figure 7.11

34
Radial Probability p293

Distribution

35
7-6 Quantum Numbers p293
 Quantum Numbers for the First Four p294

Levels of Orbitals in the Hydrogen Atom

37
 P294
Ex 7.6 Electron Subshells
For principle quantum level n = 5, determine the number
of allowed subshells (different values of l), and give the
designation of each.
Solution:
7-7 Orbital Shapes and p295

Energies

Figure 7.13

39
 p296

The Boundary Surface Representations

of All Three 2p Orbitals

Figure 7.14

40
 p296
A Summary of the Hydrogen Atom

41
7-8 Electron Spin and Pauli p296
Principle
The Boundary Surfaces of All of the 3d Orbitals

Figure 7.16 42
 p297

Figure 7.17 Representation of the 4f orbitals in terms of

their boundary surfaces.
43
Orbital energy levels p298

for the hydrogen atom

Figure 7.18

44
7-9 Polyelectronic Atoms p298

Figure 7.19
 p298

Consider the sodium atom,

which has 11 electrons.
A Comparison of the Radial p299
Probability Distributions of
the 2s and 2p Orbitals

Figure 7.20
A comparison of the radial probability 47
distributions of the 2s and 2p orbitals.
 p299
The Radial Probability
Distribution of the 3s Orbital

Figure 7.21 (a) 48

A Comparison of the Radial p299

Probability Distributions of
the 3s, 3p, and 3d Orbitals

Figure 7.21 (b) 49

1s Orbital

50
2px Orbital

51
2py Orbital

52
2pz Orbital

53
3d x2 y 2 Orbital

54
3dxy Orbital

55
3dxz Orbital

56
3dyz Orbital

57
3dz2 Orbital

58
7-10 The History of The p299

Periodic Table

Figure 7.22
The orders of the energies of the orbitals in the
first three levels of polyelectronic atoms.

59
7-11 The Aufbau Principle and p302

Periodic Table
p304
 p304
The electron configurations
Orbital Energies

63
 p305

The electron configuration of

transition metals
 p306
Electron configurations for
potassium through krypton.

Figure 7.26
Electron configurations for potassium through krypton. The transition
metals (scandium through zinc) have the general configuration
[Ar]4s24dn, except for chromium and copper.

65
 p306
The Orbitals Being Filled for Elements
in Various Parts of the Periodic Table

Figure 7.27

The orbitals being filled for electrons in various parts of the

periodic table. Note that in going along a horizontal row (a
period), the (n + 1)s orbital fills before the nd orbital. The
group labels indicate the number of valence electrons (ns
plus np electrons) foe the elements in each group. 66
 The periodic table with atomic p307
symbols, atomic numbers, and
partial electron configurations.

Figure 7.28
67
 P308
Ex 7.7 Electron Configurations
Give the electron configurations for sulfur (S), cadmium
(Cd), hafnium (Hf), and radium (Ra) using the periodic
table inside the front cover of this book.
Solution:
p308

69
7-12 Periodic Trends in Atomic p309

Properties

Ionization Energy
 p310
First Ionization Energies

71
 The Values of First Ionization p310
Energy for the Elements in the
First Six Periods

72
Figure 7.30
 Trends in Ionization p311

Energies(kJ/mol) for the

Representative elements.

Figure 7.31
73
 P311
Ex 7.8 Trends in Ionization Energies
The first ionization energy for phosphorus is 1060
KJ/mol, and that for sulfur is 1005 KJ/mol. Why?
Solution:
 Ex 7.9 Ionization Energies P311

Consider atoms with the following electron

configurations:1s22s22p6;1s22s22p63s1;1s22s22p63s2

Which atom has the largest first ionization energy, and

which one has the smallest second ionization energy?
Explain your choices.
Solution:

75
Ex 7.9 (continuous) p312
Atomic Radius of a Metal

77
Atomic Radius of a Nonmetal

78
 p312
Electron Affinity
 p313

Electron Affinities of the Halogens

80
Ex 7.10 Trends in Radii p313

Predict the trend in radius for the following ions: Be+,

Mg2+, Ca2+, and Sr2+.
Solution:
Atomic Radii for Selected Atoms p313

Figure 7.34 82
7-13 The Properties of a p314

Group: The Alkali Metal

83
Figure 7.35
 Special Names for groups p315

in the Periodic Table

84
Figure 7.35
The Alkali Metals p316

2Na(s) + Cl2(g) → 2NaCl(s)

85
 Typical reactions for the p317
nonmetal with alkali metals

The expected trend in reducing

ability: Cs > Rb > K > Na > Li

Potassium reacts violently with water.

 p318
Hydration Energies for Alkali Ions

2M(s) + 2H2O(l) → H2(g) + 2M+ + 2OH-(aq) + energy

87