Download Chapter 4-2 The Quantum Model of the Atom

Chapter 4-2
The Quantum Model of the
Atom
Coach Kelsoe
Chemistry
Pages 104–110
Electrons as Waves
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Investigations into the photoelectric
effect and hydrogen atomic
emission showed that light behaves
as a wave and as a particle.
Louis de Broglie asked if electrons
could behave the same way as light.
de Broglie suggested that electrons
be considered waves confined to the
space around the atomic nucleus.
It turns out that electrons do have
wavelike properties.
Properties of Electrons
Scientists demonstrated that electrons can
be diffracted and can interfere with each
other.
 Diffraction is the bending of a wave as it
passes by the edge of an object.
 Interference occurs when waves overlap,
which results in the reduction of energy in
some areas and an increase in others.

Heisenberg Uncertainty Principle
The idea that electrons have a
wave-particle nature bothered
scientists.
 Werner Heisenberg proposed
an idea that involved the
detection of electrons.
 The Heisenberg uncertainty
principle states that it is
impossible to determine
simultaneously both the
position and velocity of an
electron or any other particle.
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The Schrödinger Wave Equation
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In 1926, Erwin Schrödinger used the
idea that electrons act like waves and
particles to develop an equation that
treated electrons as waves.
His equation along with the
Heisenberg uncertainty principle laid
the foundation for the modern
quantum theory.
Quantum theory describes
mathematically the wave properties of
electrons and other very small
particles.
Orbits or Orbitals?
Electrons do not travel in
neat orbits around the
nucleus like Bohr said.
 Electrons exist in regions
called orbitals, threedimensional regions around
the nucleus that indicate
the probable location of an
electron.
 Orbitals have different sizes
and shapes.
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Atomic Orbitals
In Bohr’s atomic model, electrons of
increasing energy occupy orbits farther from
the nucleus.
 In Schrödinger’s equation, an electron’s
energy is not the only characteristic of an
orbital.
 In order to completely describe orbitals,
scientists use quantum numbers.

Warning!
The next nine slides may be hazardous
to your science health. Don’t
concentrate too much on the lingo.
The concepts will hit you soon. Hang
tight and understanding will come!
Quantum Numbers
Quantum numbers specify the properties
of atomic orbitals and the properties of
electrons in orbitals.
 The first three quantum numbers indicate
the main energy level, the shape, and the
orientation of an orbital.
 The fourth describes a fundamental state of
spin the electron occupies in the orbital.

Principal Quantum Number
The principal quantum number,
symbolized by n, indicates the main energy
level occupied by the electron.
 Values of n are positive integers only.
 As n increases, the electron’s energy and its
average distance from the nucleus increase.
 For example, an electron for which n=1
occupies the first, or lowest, main energy
level and is located closest to the nucleus.

Principal Quantum Numbers
More than one electron can have the same
n value. These are said to be in the same
electron shell or energy level.
 The total number of orbitals that exist in a
given energy level is equal to n2.

Angular Momentum Quantum Number
Except at the first main energy level,
orbitals of different shapes exist for a given
value of n.
 The angular momentum quantum
number, symbolized by l, indicates the
shape of the orbital.
 The number of orbital shapes possible is
equal to n.
 The values of l allowed are zero and all
positive integers less than or equal to n-1.
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Angular Momentum Quantum Number
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For example, orbitals
for which n=2 can
have one or two
shapes corresponding
to l=0 and l=1
Depending on its
value of l, an orbital is
assigned a letter.
l
Letter
0
s
1
p
2
d
3
f
Angular Momentum Quantum Number
s orbitals are round, p are shaped like 2
teardrops, and d orbitals are more complex.
 So in the first energy level (n=1), there is
only one orbital possible – an s orbital.
 In the second energy level (n=2), there are
two possible orbitals – s and p orbitals.
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Angular Momentum Quantum Number
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Each atomic orbital is
designated by the
principal quantum
number followed by
the letter of the
orbital.
Magnetic Quantum Number
Atomic orbitals can have the same shape
but different orientations.
 The magnetic quantum number,
symbolized by m, indicates the orientation
of an orbital around the nucleus.
 Because the s orbital is spherical and is
centered around the nucleus, it has only
one orientation.
 The possible orientations are aligned along
the x, y, or z axis
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Spin Quantum Number
An electron in an orbital can be thought of
as spinning on an internal axis.
 Electrons spin in one of two possible
directions.
 The spin quantum number has only two
possible values, which indicate the two
fundamental spin states of an electron in an
orbital.
 A single orbital can hold a maximum of two
electrons, which must have opposite spins.

Congratulations!
You made it through the rough
stuff! The next table will help
clarify everything covered in the
last nine sides. KNOW THE
TABLE!
Quantum Number Relationships in
Atomic Structure
Principle
Quantum
Number
(n)
Orbitals in
Main
Energy
Level (n
orbitals)
#Orbitals
per
Sublevel
# Orbitals
per Main
Energy
Level (n2)
#
Electrons
per
Orbital
# Electrons
per Main
Energy
Level (2n2)
1
s
1
1
2
2
2
s
p
1
3
4
2
6
8
3
s
p
d
1
3
5
9
2
6
10
18
4
s
p
d
f
1
3
5
7
16
2
6
10
14
32