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5.3 Atomic Emission Spectra and the Quantum
Mechanical Model
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
1
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5.3 Atomic Emission Spectra and the Quantum
Mechanical Model
CHEMISTRY
& YOU
What gives gas-filled lights their colors?
An electric current
passing through the gas
in each glass tube
makes the gas glow with
its own characteristic
color.
2
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and Atomic
> Light
Emission Spectra
5.3 Atomic Emission Spectra and the Quantum
Mechanical Model
Light and Atomic Emission Spectra
What causes atomic emission
spectra?
3
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and Atomic Emission
> Light
Spectra
5.3 Atomic Emission Spectra and the Quantum
Mechanical Model
The Nature of Light
4
•
By the year 1900, there was enough
experimental evidence to convince scientists
that light consisted of waves.
•
The amplitude of a wave is the wave’s height
from zero to the crest.
•
The wavelength, represented by λ (the Greek
letter lambda), is the distance between the
crests.
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and Atomic Emission
> Light
Spectra
5.3 Atomic Emission Spectra and the Quantum
Mechanical Model
The Nature of Light
• The frequency, represented by ν (the
Greek letter nu), is the number of wave
cycles to pass a given point per unit of
time.
• The SI unit of cycles per second is called
the hertz (Hz).
5
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and Atomic Emission
> Light
Spectra
5.3 Atomic Emission Spectra and the Quantum
Mechanical Model
The Nature of Light
The product of frequency and wavelength
equals a constant (c), the speed of light.
c = λν
6
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and Atomic Emission
> Light
Spectra
5.3 Atomic Emission Spectra and the Quantum
Mechanical Model
The frequency (ν) and wavelength (λ) of
light are inversely proportional to each
other. As the wavelength increases, the
frequency decreases.
7
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and Atomic Emission
> Light
Spectra
5.3 Atomic Emission Spectra and the Quantum
Mechanical Model
The Nature of Light
According to the wave model, light consists of
electromagnetic waves.
• Electromagnetic radiation includes
radio waves, microwaves, infrared
waves, visible light, ultraviolet waves,
X-rays, and gamma rays.
• All electromagnetic waves travel in a
vacuum at a speed of 2.998 × 108 m/s.
8
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and Atomic Emission
> Light
Spectra
5.3 Atomic Emission Spectra and the Quantum
Mechanical Model
The Nature of Light
The sun and incandescent light bulbs emit white
light, which consists of light with a continuous
range of wavelengths and frequencies.
• When sunlight passes through a prism, the
different wavelengths separate into a
spectrum of colors.
• In the visible spectrum, red light has the
longest wavelength and the lowest
frequency.
9
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and Atomic Emission
> Light
Spectra
5.3 Atomic Emission Spectra and the Quantum
Mechanical Model
The electromagnetic spectrum consists of
radiation over a broad range of wavelengths.
Low energy
(λ = 700 nm)
Frequency ν (s-1)
3 x 106
102
Wavelength λ (m)
10
High energy
(λ = 380 nm)
3 x 1012
3 x 1022
10-8
10-14
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and Atomic Emission
> Light
Spectra
5.3 Atomic Emission Spectra and the Quantum
Mechanical Model
Atomic Emission Spectra
When atoms absorb energy, their
electrons move to higher energy levels.
These electrons lose energy by
emitting light when they return to lower
energy levels.
11
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and Atomic
> Light
Emission Spectra
5.3 Atomic Emission Spectra and the Quantum
Mechanical Model
Atomic Emission Spectra
A prism separates light into the colors it
contains. White light produces a rainbow
of colors.
Screen
Light
bulb
12
Slit
Prism
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5.3 Atomic Emission Spectra and the Quantum
Mechanical Model
Sample Problem 5.2
Calculating the Wavelength of Light
Calculate the wavelength of the
yellow light emitted by a sodium
lamp if the frequency of the
radiation is 5.09 × 1014 Hz.
13
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5.3 Atomic Emission Spectra and the Quantum
Mechanical Model
Sample Problem 5.2
1 Analyze List the knowns and the unknown.
Use the equation c = λν to solve for the
unknown wavelength.
KNOWNS
frequency (ν) = 5.09 × 1014 /s
c = 2.998 × 108 m/s
UNKNOWN
wavelength (λ) = ? m
14
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5.3 Atomic Emission Spectra and the Quantum
Mechanical Model
Sample Problem 5.2
2 Calculate Solve for the unknown.
Write the expression that relates the
frequency and wavelength of light.
c = λν
15
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5.3 Atomic Emission Spectra and the Quantum
Mechanical Model
Sample Problem 5.2
2 Calculate Solve for the unknown.
Rearrange the equation to solve for λ.
c = λν
c
λ= ν
16
Solve for λ by dividing both
sides by ν:
λν
c
ν = ν
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5.3 Atomic Emission Spectra and the Quantum
Mechanical Model
Sample Problem 5.2
2 Calculate Solve for the unknown.
Substitute the known values for ν and c into
the equation and solve.
c
2.998 × 108 m/s
λ=
=
= 5.89 × 10–7 m
14
ν
5.09 × 10 /s
17
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5.3 Atomic Emission Spectra and the Quantum
Mechanical Model
What is the frequency of a red laser
that has a wavelength of 676 nm?
18
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5.3 Atomic Emission Spectra and the Quantum
Mechanical Model
What is the frequency of a red laser
that has a wavelength of 676 nm?
c = λν
ν=
c
λ
c 2.998 × 108 m/s
ν = λ = 6.76 × 10–7 /s = 4.43 × 1014 m
19
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5.3 Atomic Emission Spectra and the Quantum
Mechanical Model
The Quantum Concept
and Photons
The Quantum Concept and Photons
How did Einstein explain the
photoelectric effect?
20
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5.3 Atomic Emission Spectra and the Quantum
Mechanical Model
The Quantum Concept
and Photons
The Quantization of Energy
German physicist Max Planck (1858–1947)
showed mathematically that the amount of
radiant energy (E) of a single quantum
absorbed or emitted by a body is proportional
to the frequency of radiation (ν).
E
21
ν or E = hν
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5.3 Atomic Emission Spectra and the Quantum
Mechanical Model
The Quantum Concept
and Photons
The Quantization of Energy
The constant (h), which has a value of 6.626 ×
10–34 J·s (J is the joule, the SI unit of energy),
is called Planck’s constant.
E
22
νEor Eν=orhνE = hν
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5.3 Atomic Emission Spectra and the Quantum
Mechanical Model
The Quantum Concept
and Photons
The Photoelectric Effect
Albert Einstein used Planck’s quantum theory to
explain the photoelectric effect.
In the photoelectric effect, electrons
are ejected when light shines on a
metal.
23
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5.3 Atomic Emission Spectra and the Quantum
Mechanical Model
The Quantum Concept
and Photons
The Photoelectric Effect
To explain the photoelectric effect,
Einstein proposed that light could be
described as quanta of energy that
behave as if they were particles.
24
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5.3 Atomic Emission Spectra and the Quantum
Mechanical Model
The Quantum Concept
and Photons
The Photoelectric Effect
These light quanta are called photons.
• Einstein’s theory that light behaves as a stream
of particles explains the photoelectric effect and
many other observations.
25
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5.3 Atomic Emission Spectra and the Quantum
Mechanical Model
The Quantum Concept
and Photons
The Photoelectric Effect
These light quanta are called photons.
• Einstein’s theory that light behaves as a stream
of particles explains the photoelectric effect and
many other observations.
• Light behaves as waves in other situations; we
must consider that light possesses both
wavelike and particle-like properties.
26
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5.3 Atomic Emission Spectra and the Quantum
Mechanical Model
The Quantum Concept
and Photons
The Photoelectric Effect
No electrons are ejected
because the frequency of
the light is below the
threshold frequency.
27
If the light is at or above
the threshold frequency,
electrons are ejected.
If the frequency is
increased, the ejected
electrons will travel faster.
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Explanation of
> An
Atomic Spectra
5.3 Atomic Emission Spectra and the Quantum
Mechanical Model
When an electron has its lowest possible
energy, the atom is in its ground state.
• In the ground state, the principal quantum
number (n) is 1.
28
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Explanation of
> An
Atomic Spectra
5.3 Atomic Emission Spectra and the Quantum
Mechanical Model
When an electron has its lowest possible
energy, the atom is in its ground state.
• In the ground state, the principal quantum
number (n) is 1.
• Excitation of the electron by absorbing
energy raises the atom to an excited state
with n = 2, 3, 4, 5, or 6, and so forth.
• A quantum of energy in the form of light is
emitted when the electron drops back to a
lower energy level.
29
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5.3 Atomic Emission Spectra and the Quantum
Mechanical Model
Quantum Mechanics
The Heisenberg Uncertainty Principle
The Heisenberg uncertainty principle states
that it is impossible to know both the velocity
and the position of a particle at the same time.
30
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5.3 Atomic Emission Spectra and the Quantum
Mechanical Model
Quantum Mechanics
The Heisenberg Uncertainty Principle
The Heisenberg uncertainty principle states
that it is impossible to know both the velocity
and the position of a particle at the same time.
• This limitation is critical when dealing with
small particles such as electrons.
• But it does not matter for ordinary-sized
objects such as cars or airplanes.
31
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5.3 Atomic Emission Spectra and the Quantum
Mechanical Model
•
To locate an electron, you might strike it with a photon.
•
The electron has such a small mass that striking it with a photon affects its
motion in a way that cannot be predicted accurately.
•
The very act of measuring the position of the electron changes its velocity,
making its velocity uncertain.
Before collision:
A photon strikes
an electron during
an attempt to
observe the
electron’s position.
32
Quantum Mechanics
After collision:
The impact
changes the
electron’s velocity,
making it
uncertain.
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5.3 Atomic Emission Spectra and the Quantum
Mechanical Model
The Heisenberg uncertainty principle
states that it is impossible to
simultaneously know which two
attributes of a particle?
33
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5.3 Atomic Emission Spectra and the Quantum
Mechanical Model
The Heisenberg uncertainty principle
states that it is impossible to
simultaneously know which two
attributes of a particle?
velocity and position
34
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5.3 Atomic Emission Spectra and the Quantum
Mechanical Model
Key Concepts and
Key Equations
When atoms absorb energy, their electrons move
to higher energy levels. These electrons lose
energy by emitting light when they return to lower
energy levels.
To explain the photoelectric effect, Einstein
proposed that light could be described as quanta
of energy that behave as if they were particles.
The light emitted by an electron moving from a
higher to a lower energy level has a frequency
directly proportional to the energy change of the
electron.
35
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5.3 Atomic Emission Spectra and the Quantum
Mechanical Model
Key Concepts and
Key Equations
Classical mechanics adequately describes the
motions of bodies much larger than atoms,
while quantum mechanics describes the
motions of subatomic particles and atoms as
waves.
C = λν
E=h×ν
36
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5.3 Atomic Emission Spectra and the Quantum
Mechanical Model
Glossary Terms
• amplitude: the height of a wave’s crest
• wavelength: the distance between adjacent
crests of a wave
• frequency: the number of wave cycles that
pass a given point per unit of time; frequency
and wavelength are inversely proportional to
each other
• hertz: the unit of frequency, equal to one
cycle per second
37
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5.3 Atomic Emission Spectra and the Quantum
Mechanical Model
Glossary Terms
• electromagnetic radiation: energy waves
that travel in a vacuum at a speed of 2.998 ×
108 m/s; includes radio waves, microwaves,
infrared waves, visible light, ultraviolet waves,
X-rays, and gamma rays
• spectrum: wavelengths of visible light that
are separated when a beam of light passes
through a prism; range of wavelengths of
electromagnetic radiation
38
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5.3 Atomic Emission Spectra and the Quantum
Mechanical Model
Glossary Terms
• atomic emission spectrum: the pattern
formed when light passes through a prism or
diffraction grating to separate it into the
different frequencies of light it contains
• Planck’s constant: the constant (h) by which
the amount of radiant energy (E) is
proportional to the frequency of the radiation
(ν)
• photoelectric effect: the phenomenon in
which electrons are ejected when light shines
on a metal
39
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5.3 Atomic Emission Spectra and the Quantum
Mechanical Model
Glossary Terms
• photon: a quantum of light; a discrete bundle
of electromagnetic energy that interacts with
matter similarly to particles
• ground state: the lowest possible energy of
an atom described by quantum mechanics
• Heisenberg uncertainty principle: it is
impossible to know both the velocity and the
position of a particle at the same time
40
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5.3 Atomic Emission Spectra and the Quantum
Mechanical Model
BIG IDEA
Electrons and the Structure of Atoms
• Electrons can absorb energy to move from
one energy level to a higher energy level.
• When an electron moves from a higher
energy level back down to a lower energy
level, light is emitted.
41
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5.3 Atomic Emission Spectra and the Quantum
Mechanical Model
END OF 5.3
42
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