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Chapter 4
Arrangement of Electrons in Atoms
Table of Contents
Section 1 The Development of a New Atomic Model
Section 2 The Quantum Model of the Atom
Section 3 Electron Configurations
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Chapter 4
Section 1 The Development of a New
Atomic Model
Objectives
• Explain the mathematical relationship among the
speed, wavelength, and frequency of
electromagnetic radiation.
• Discuss the dual wave-particle nature of light.
• Discuss the significance of the photoelectric effect
and the line-emission spectrum of hydrogen to the
development of the atomic model.
• Describe the Bohr model of the hydrogen atom.
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Chapter 4
Section 1 The Development of a New
Atomic Model
Properties of Light
The Wave Description of Light
• Electromagnetic radiation is a form of energy that
exhibits wavelike behavior as it travels through
space.
• Together, all the forms of electromagnetic radiation
form the electromagnetic spectrum.
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Chapter 4
Section 1 The Development of a New
Atomic Model
Electromagnetic Spectrum
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Chapter 4
Section 1 The Development of a New
Atomic Model
Properties of Light, continued
• Wavelength () is the distance between
corresponding points on adjacent waves.
• Frequency (v) is defined as the number of waves
that pass a given point in a specific time, usually one
second.
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Chapter 4
Section 1 The Development of a New
Atomic Model
Wavelength and Frequency
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Chapter 4
Section 1 The Development of a New
Atomic Model
Properties of Light, continued
• Frequency and wavelength are mathematically related
to each other:
c = v
• In the equation,
• c = speed of light (in m/s) 3.00 X 108
•  = wavelength = (in m)
• v = frequency = (in s1 or Hz).
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Properties of light, continued
What is the relationship between wavelength and
frequency?
Sample problems:
1. What is the wavelength of the yellow sodium
emission, which has a frequency of 5.09 X 10 14 Hz?
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Properties of light continued
Sample #2
What is the frequency of violet light with a wavelength of
408 nm?
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Chapter 4
Section 1 The Development of a New
Atomic Model
The Photoelectric Effect
• The photoelectric effect refers to the emission
of electrons from a metal when light shines on
the metal.
• Couldn’t be explained with the wave theory of
light.
• Example- 3 baseballs vs. 12 ping pong balls
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Chapter 4
Section 1 The Development of a New
Atomic Model
Photoelectric Effect
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Properties of light
The Particle Description of Light
• Each particle of light contains a specific amount of
energy (quanta).
• Einstein called these light packets photons
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Chapter 4
Section 1 The Development of a New
Atomic Model
The Photoelectric Effect, continued
The Particle Description of Light, continued
• German physicist Max Planck proposed the following
relationship between a quantum of energy and the frequency
of radiation:
E = hv
• E = energy, in joules
• v = frequency, in s−1
• h is constant known as Planck’s constant;
• h = 6.626  1034 J• s.
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Chapter 4
Section 1 The Development of a New
Atomic Model
The Photoelectric Effect, continued
The Particle Description of Light, continued
• A photon is a particle of electromagnetic
radiation having zero mass and carrying a
quantum of energy.
• The energy of a particular photon is directly
proportional to the frequency.
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Particle description of light
Sample problems
#1 What is the energy per photon of radiation with a
frequency of 6.75 X 10 15 Hz?
#2 The spectral line of lithium occurs at 671 nm.
Calculate the energy of this light.
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Chapter 4
Section 1 The Development of a New
Atomic Model
Bohr Model of the atom
-Bohr studied hydrogen gas
-noted that hydrogen’s emission spectrum had
certain lines
-he said these must represent specific energy
levels in the hydrogen atom
-Problem-doesn’t work for atoms with more
than one electron
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Chapter 4
Section 1 The Development of a New
Atomic Model
Hydrogen’s Line-Emission Spectrum
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Chapter 4
Section 1 The Development of a New
Atomic Model
Bohr Model of the Hydrogen Atom, continued
• When an electron falls to a lower energy level, a
photon is emitted, and the process is called
emission.
• Energy must be added to an atom in order to move
an electron from a lower energy level to a higher
energy level. This process is called absorption.
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Chapter 4
Section 1 The Development of a New
Atomic Model
Photon Emission and Absorption
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Chapter 4
Section 2 The Quantum Model of
the Atom
Objectives
• Discuss Louis de Broglie’s role in the development
of the quantum model of the atom.
• Compare and contrast the Bohr model and the
quantum model of the atom.
• Explain how the Heisenberg uncertainty principle
and the Schrödinger wave equation led to the idea
of atomic orbitals.
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Chapter 4
Section 2 The Quantum Model of
the Atom
Objectives, continued
• List the four quantum numbers and describe their
significance.
• Relate the number of sublevels corresponding to
each of an atom’s main energy levels, the number
of orbitals per sublevel, and the number of orbitals
per main energy level.
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Chapter 4
Section 2 The Quantum Model of
the Atom
Electrons as Waves
• If light can act as waves or particles, electrons can
act as a particle or wave
• French scientist Louis de Broglie suggested that
electrons be considered waves confined to the
space around an atomic nucleus.
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Chapter 4
Section 2 The Quantum Model of
the Atom
The Heisenberg Uncertainty Principle
• German physicist Werner Heisenberg proposed that
it is impossible to study both the position and velocity
of an electron at the same time---- this is known as
• Heisenberg uncertainty principle
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Chapter 4
Section 2 The Quantum Model of
the Atom
The Schrödinger Wave Equation
• In 1926, Austrian physicist Erwin Schrödinger
developed an equation that treated electrons in
atoms as waves.
• Together with the Heisenberg uncertainty principle,
the Schrödinger wave equation laid the foundation
for modern quantum theory.
• Quantum theory describes mathematically the
wave properties of electrons and other very small
particles.
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Chapter 4
Section 2 The Quantum Model of
the Atom
The Schrödinger Wave Equation, continued
• Electrons do not travel around the nucleus in neat
orbits, as Bohr had postulated.
• Instead, they exist in certain regions called orbitals.
• An orbital is a three-dimensional region around the
nucleus that indicates the probable location of an
electron.
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Chapter 4
Section 2 The Quantum Model of
the Atom
Atomic Orbitals and Quantum Numbers
• Quantum numbers specify the properties of atomic
orbitals and the properties of electrons in orbitals.
• This is an electron’s address• no two electrons in an atom have the same 4
quantum numbers.
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Quantum numbers
• The principal quantum number, symbolized by n, indicates the
main energy level occupied by the electron.
• The angular momentum quantum number, symbolized by l,
indicates the shape of the orbital.
• The magnetic quantum number, symbolized by m, indicates the
orientation of an orbital around the nucleus.
• The spin quantum number has only two possible values—(+1/2 ,
1/2)—which indicate the two fundamental spin states of an
electron in an orbital.
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Chapter 4
Section 3 Electron Configurations
Objectives
• List the total number of electrons needed to fully
occupy each main energy level.
• State the Aufbau principle, the Pauli exclusion
principle, and Hund’s rule.
• Describe the electron configurations for the atoms of
any element using orbital notation, electronconfiguration notation, and, when appropriate, noblegas notation.
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Chapter 4
Section 3 Electron Configurations
Electron Configurations
• The arrangement of electrons in an atom is known
as the atom’s electron configuration.
• The lowest-energy arrangement of the electrons
for each element is called the element’s groundstate electron configuration.
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Chapter 4
Section 3 Electron Configurations
Rules Governing Electron Configurations
• According to the Aufbau principle, an electron
occupies the lowest-energy orbital that can receive it.
• According to the Pauli exclusion principle, no two
electrons in the same atom can have the same set of
four quantum numbers.
• According to Hund’s rule, orbitals of equal energy are
each occupied by one electron before any orbital is
occupied by a second electron
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