Atomic Model

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Chapter 5
Electrons In Atoms
5.1 Revising the Atomic Model
5.2 Electron Arrangement in Atoms
5.3 Atomic Emission Spectra and
the Quantum Mechanical Model

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Shown here is a life-
sized model of a skier,
but not all models are
physical. In fact, the
current model of the
atom is a mathematical
model.
CHEMISTRY & YOU
Why do scientists use mathematical
models to describe the position of
electrons in atoms?

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What did Bohr propose in
his model of the atom?
Energy Levels in Atoms
Energy Levels in Atoms

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Energy Levels in Atoms
• It explained only a few simple
properties of atoms.
Limitations of Rutherford’s Atomic Model

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Energy Levels in Atoms
Limitations of Rutherford’s Atomic Model
• It explained only a few simple
properties of atoms.
• It could not explain the chemical
properties of elements.

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Energy Levels in Atoms
• It explained only a few simple
properties of atoms.
• It could not explain the chemical
properties of elements.
For example, Rutherford’s model
could not explain why an object
such as the iron scroll shown here
first glows dull red, then yellow,
and then white when heated to
higher and higher temperatures.
Limitations of Rutherford’s Atomic Model

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Energy Levels in Atoms
In 1913, Niels Bohr (1885–1962), a young
Danish physicist and a student of Rutherford,
developed a new atomic model.
• He changed Rutherford’s model to
incorporate newer discoveries about
how the energy of an atom changes
when the atom absorbs or emits
light.
The Bohr Model

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Energy Levels in Atoms
Bohr proposed that an electron
is found only in specific circular
paths, or orbits, around the
nucleus.
The Bohr Model

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Each possible electron orbit in Bohr’s
model has a fixed energy.
Energy Levels in Atoms
The Bohr Model

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Each possible electron orbit in Bohr’s
model has a fixed energy.
Energy Levels in Atoms
• The fixed energies an electron can
have are called energy levels.
The Bohr Model

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Each possible electron orbit in Bohr’s
model has a fixed energy.
Energy Levels in Atoms
• The fixed energies an electron can
have are called energy levels.
• A quantum of energy is the amount of
energy required to move an electron
from one energy level to another
energy level.
The Bohr Model

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Energy Levels in Atoms
The rungs on this ladder are somewhat
like the energy levels in Bohr’s model of
the atom.
• A person on a ladder
cannot stand between
the rungs. Similarly, the
electrons in an atom
cannot exist between
energy levels.
The Bohr Model

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Energy Levels in Atoms
The rungs on this ladder are somewhat
like the energy levels in Bohr’s model of
the atom.
The Bohr Model
• The energy levels in
atoms are unequally
spaced, like the rungs in
this unusual ladder. The
higher energy levels are
closer together.

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How does the Bohr model improve
upon the Rutherford model?

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How does the Bohr model improve
upon the Rutherford model?
The Rutherford model could not explain why
elements that have been heated to higher
and higher temperatures give off different
colors of light. The Bohr model explains
how the energy levels of electrons in an
atom change when the atom emits light.

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What does the quantum
mechanical model determine
about the electrons in an atom?
The Quantum
Mechanical Model
The Quantum Mechanical Model

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• Austrian physicist Erwin Schrödinger (1887–
1961) used new theoretical calculations and
experimental results to devise and solve a
mathematical equation describing the
behavior of the electron in a hydrogen atom.
• The modern description of the electrons in
atoms, the quantum mechanical model,
came from the mathematical solutions to the
Schrödinger equation.
The Quantum
Mechanical Model

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The Quantum
Mechanical Model
• Like the Bohr model, the quantum
mechanical model of the atom restricts
the energy of electrons to certain
values.
• Unlike the Bohr model, however, the
quantum mechanical model does not
specify an exact path the electron takes
around the nucleus.

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The quantum mechanical model
determines the allowed energies
an electron can have and how
likely it is to find the electron in
various locations around the
nucleus of an atom.
The Quantum
Mechanical Model

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Probability describes how likely it is to find
an electron in a particular location around
the nucleus of an atom.
The Quantum
Mechanical Model

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• In the quantum mechanical
model, the probability of
finding an electron within a
certain volume of space
surrounding the nucleus
can be represented as a
fuzzy cloudlike region.
• The cloud is more dense
where the probability of
finding the electron is high.
The Quantum
Mechanical Model
Electron cloud

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How are the quantum mechanical
model and the Bohr model alike?
How are they different?

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How are the quantum mechanical
model and the Bohr model alike?
How are they different?
Like the Bohr model, the quantum
mechanical model restricts the energy of
electrons to certain values. Unlike the
Bohr model, the quantum mechanical
model does not specify an exact path the
electron takes around the nucleus.

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Atomic Orbitals
Atomic Orbitals
How do sublevels of principal
energy levels differ?

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Atomic Orbitals
• Solutions to the Schrödinger equation give
the energies, or energy levels, an electron
can have.

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Atomic Orbitals
• Solutions to the Schrödinger equation give
the energies, or energy levels, an electron
can have.
• For each energy level, the Schrödinger
equation also leads to a mathematical
expression, called an atomic orbital.

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Atomic Orbitals
• Solutions to the Schrödinger equation give
the energies, or energy levels, an electron
can have.
• For each energy level, the Schrödinger
equation also leads to a mathematical
expression, called an atomic orbital.
• An atomic orbital is represented pictorially
as a region of space in which there is a
high probability of finding an electron.

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Atomic Orbitals
• The energy levels of electrons in the
quantum mechanical model are labeled
by principal quantum numbers (n).

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Atomic Orbitals
• The energy levels of electrons in the
quantum mechanical model are labeled
by principal quantum numbers (n).
• These numbers are assigned the values
n = 1, 2, 3, 4, and so forth.

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Atomic Orbitals
• The energy levels of electrons in the
quantum mechanical model are labeled
by principal quantum numbers (n).
• These numbers are assigned the values
n = 1, 2, 3, 4, and so forth.
• For each principal energy level greater
than 1, there are several orbitals with
different shapes and at different energy
levels.

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Atomic Orbitals
• The energy levels of electrons in the
quantum mechanical model are labeled
by principal quantum numbers (n).
• These numbers are assigned the values
n = 1, 2, 3, 4, and so forth.
• For each principal energy level greater
than 1, there are several orbitals with
different shapes and at different energy
levels.
• These energy levels within a principal
energy level constitute energy sublevels.

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Each energy sublevel corresponds
to one or more orbitals of different
shapes. The orbitals describe
where an electron is likely to be
found.
Atomic Orbitals

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Atomic Orbitals
• The s orbitals are spherical.
Different atomic orbitals are denoted by
letters.

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Atomic Orbitals
• The s orbitals are spherical.
• The p orbitals are dumbbell-shaped.
Different atomic orbitals are denoted by
letters.

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Atomic Orbitals
For a given principal energy level
greater than 1, there is one s orbital…

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Atomic Orbitals
For a given principal energy level
greater than 1, there is one s orbital, 3
p orbitals...

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Atomic Orbitals
For a given principal energy level
greater than 1, there is one s orbital, 3
p orbitals, and 5 d orbitals.

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Atomic Orbitals
Four of the five d orbitals have the same
shape but different orientations in space.

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Atomic Orbitals
Summary of Principal Energy Levels and Sublevels
Principal
energy level
Number of
sublevels
Type of sublevel
Maximum
number of
electrons
n = 1 1 1s (1 orbital) 2
n = 2 2 2s (1 orbital), 2p (3 orbitals) 8
n = 3 3
3s (1 orbital), 3p (3 orbitals),
3d (5 orbitals)
18
n = 4 4
4s (1 orbital), 4p (3 orbitals),
4d (5 orbitals), 4f (7 orbitals)
32
The numbers and types of atomic orbitals
depend on the principal energy level.

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Atomic Orbitals
• The principal quantum number, n, always
equals the number of sublevels within that
principal energy level.

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Atomic Orbitals
• The principal quantum number, n, always
equals the number of sublevels within that
principal energy level.
• The number of orbitals in a principal
energy level is equal to n2.

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Atomic Orbitals
• The principal quantum number, n, always
equals the number of sublevels within that
principal energy level.
• The number of orbitals in a principal
energy level is equal to n2.
• A maximum of two electrons can occupy
an orbital.

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Atomic Orbitals
• The principal quantum number, n, always
equals the number of sublevels within that
principal energy level.
• The number of orbitals in a principal
energy level is equal to n2.
• A maximum of two electrons can occupy
an orbital.
• Therefore, the maximum number of
electrons that can occupy a principal
energy level is given by the formula 2n2.

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Calculate the maximum number of
electrons in the 5th principal energy
level (n = 5).

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Calculate the maximum number of
electrons in the 5th principal energy
level (n = 5).
The maximum number of electrons that can
occupy a principal energy level is given by
the formula 2n2. If n = 5, 2n2 = 50.

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CHEMISTRY & YOU
Why do scientists no longer use
physical models to describe the motion
of electrons?

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• Previous models of the atom were physical models
based on the motion of large objects.
• Theoretical calculations and experimental results
showed that these models did not always correctly
describe electron motion.
• Schrödinger devised a mathematical equation
describing the behavior of the electron in a hydrogen
atom. The quantum mechanical model came from the
solutions to the Schrödinger equation.
CHEMISTRY & YOU
Why do scientists no longer use
physical models to describe the motion
of electrons?

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Key Concepts
Bohr proposed that an electron is found only in
specific circular paths, or orbits, around the
nucleus.
The quantum mechanical model determines
the allowed energies an electron can have and
how likely it is to find the electron in various
locations around the nucleus of an atom.
Each energy sublevel corresponds to one or
more orbitals of different shapes, which
describe where the electron is likely to be
found.

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Glossary Terms
• energy level: the specific energies an
electron in an atom or other system can
have
• quantum: the amount of energy needed to
move an electron from one energy level to
another

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Glossary Terms
• quantum mechanical model: the modern
description, primarily mathematical, of the
behavior of electrons in atoms
• atomic orbital: a mathematical expression
describing the probability of finding an
electron at various locations; usually
represented by the region of space around
the nucleus where there is a high probability
of finding an electron

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Electrons and the Structure of Atoms
BIG IDEA
• The quantum mechanical model of the atom
comes from the solutions to the Schrödinger
equation.
• Solutions to the Schrödinger equation give
the energies an electron can have and the
atomic orbitals, which describe the regions
of space where an electron may be found.

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END OF 5.1