Transcript 5.3 Atomic Emission Spectra and the Quantum Mechanical Model

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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Objectives
1. Explain light and atomic emission
spectra
2. Calculate wavelength or frequency
3. Describe Einstein’s explanation of
the photoelectric effect
4. Explain how the frequencies of light
emitted by an atom are related to
changes of electron energies
5. Distinguish between quantum
mechanics and classical mechanics
2
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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.
3
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Light and Atomic
Emission Spectra
Light and Atomic Emission Spectra
What causes atomic emission spectra?
spectrum: wavelengths of visible light that are
separated when a beam of light passes
through a prism; range of wavelengths of
electromagnetic radiation.
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.
4
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Light and Atomic
Emission Spectra
The Nature of Light
• By the year 1900, there was enough
experimental evidence to convince
scientists that light consisted of waves (a
disturbance or variation that transfers
energy progressively from point to point,
Merriam-Webster’s dictionary).
• The amplitude of a wave is the wave’s
height from zero to the crest.
• The wavelength, represented by  (the
Greek letter lambda), is the distance
between the crests.
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Light and Atomic
Emission Spectra
The Nature of Light
• The frequency, represented by 
(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).
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Light and Atomic
Emission Spectra
The Nature of Light
The product of frequency and
wavelength equals a constant (c), the
speed of light.
c = 
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Light and Atomic
Emission Spectra
The frequency () and wavelength () of
light are inversely proportional to each
other. As the wavelength increases, the
frequency decreases.
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Light and Atomic
Emission Spectra
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.
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Light and Atomic
Emission Spectra
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.
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Light and Atomic
Emission Spectra
The electromagnetic spectrum consists of
radiation over a broad range of wavelengths.
Low energy
( = 700 nm)
Frequency  (s-1)
3 x 106
102
Wavelength  (m)
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High energy
( = 380 nm)
3 x 1012
3 x 1022
10-8
10-14
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Light and Atomic
Emission Spectra
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.
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Light and Atomic
Emission Spectra
Atomic Emission Spectra
A prism separates light into the colors it
contains. White light produces a rainbow
of colors.
Screen
Light
bulb
13
Slit
Prism
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Light and Atomic
Emission Spectra
Atomic Emission Spectra
Light from a helium lamp produces
discrete lines.
Screen
Helium
lamp
14
Slit
Prism
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Light and Atomic
Emission Spectra
Atomic Emission Spectra
• The energy absorbed by an electron for it to
move from its current energy level to a higher
energy level is _______to
identical the energy of the light
emitted by the electron as it drops back to its
original energy level.
• The wavelengths of the spectral lines are
characteristic of the element, and they make up
_____________
the atomic emission spectrum of the element.
same emission
• No two elements have the _______
spectrum.
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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
(5.09 × 1014/s).
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Sample Problem 5.2
1 Analyze List the knowns and the unknown.
 to solve for the
Use the equation c = ____
unknown wavelength.
KNOWNS
frequency () = 5.09 × 1014 /s
c = 2.998 × 108 m/s
UNKNOWN
wavelength () = ? m
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Sample Problem 5.2
2 Calculate Solve for the unknown.
Rearrange the equation to solve for .
c = 
c
= 
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Solve for  by dividing
both sides by :
c

 = 
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Sample Problem 5.2
2 Calculate Solve for the unknown.
Substitute the known values for  and c into
the equation and solve.
c
2.998  108 m/s
–7 m
=
=
=
5.89

10

5.09  1014 /s
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Sample Problem 5.2
3 Evaluate Does the answer make sense?
The magnitude of the frequency is much
larger than the numerical value of the
speed of light, so the answer should be
much less than 1. The answer should have
3 significant figures.
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What is the frequency of a red laser
that has a wavelength of 676 nm?
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What is the frequency of a red laser
that has a wavelength of 676 nm?
c = 
c
=

c 2.998  108 m/s
 =  = 6.76  10–7 /s = 4.43  1014 m
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The Quantum Concept
and Photons
The Quantum Concept and Photons
How did Einstein explain
the photoelectric effect?
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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 ().
E
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 or E = h
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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
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 or E = h
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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.
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The Quantum Concept
and Photons
The Photoelectric Effect
Not just any frequency of light will
cause the photoelectric effect.
• Red light will not cause potassium to eject
electrons, no matter how intense the light.
• Yet a very weak yellow light shining on
potassium begins the effect.
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The Quantum Concept
and Photons
The Photoelectric Effect
• The photoelectric effect could not be
explained by classical physics.
• Classical physics correctly described light
as a form of energy.
• But, it assumed that under weak light of any
wavelength, an electron in a metal should
eventually collect enough energy to be
ejected.
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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.
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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
wave-like and particle-like properties.
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The Quantum Concept
and Photons
The Photoelectric Effect
No electrons are ejected
because the frequency of
the light is below the
threshold frequency.
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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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Sample Problem 5.3
Calculating the Energy of a Photon
What is the energy of
a photon of
microwave radiation
with a frequency of
3.20 × 1011/s?
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Sample Problem 5.3
1 Analyze List the knowns and the unknown.
Use the equation E = _____
h ×  to calculate
the energy of the photon.
KNOWNS
frequency () = 3.20 × 1011/s
h = 6.626 × 10–34 J·s
UNKNOWN
energy (E) = ? J
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Sample Problem 5.3
2 Calculate Solve for the unknown.
Substitute the known values for  and h
into the equation and solve.
E = h = (6.626  10–34 J·s)  (3.20  1011/s)
= 2.12  10–22 J
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Sample Problem 5.3
3 Evaluate Does the result make sense?
Individual photons have very
small energies, so the answer
seems reasonable.
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What is the frequency of a photon
whose energy is 1.166  10–17 J?
E = ______
 = _____
 = ________________________________
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What is the frequency of a photon
whose energy is 1.166  10–17 J?
E = h
E
=
h
E 6.626  10–34 J
 = h = 1.166  10–17 J·s = 1.760  1016 Hz
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An Explanation of
Atomic Spectra
An Explanation of Atomic Spectra
How are the frequencies of light
emitted by an atom related to
changes of electron energies?
38
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An Explanation of
Atomic Spectra
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.
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An Explanation of
Atomic Spectra
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.
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An Explanation of
Atomic Spectra
The three groups of lines in the hydrogen
spectrum correspond to the transition of
electrons from higher energy levels to lower
energy levels.
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CHEMISTRY
& YOU
The glass tubes in lighted signs contain helium,
neon, argon, krypton, or xenon gas, or a mixture
of these gases. Why do the colors of the light
depend on the gases that are used?
Each different gas has
its own characteristic
emission spectrum,
creating different colors
of light when excited
electrons return to the
ground state.
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In the hydrogen spectrum, which of
the following transitions produces a
spectral line of the greatest energy?
A. n = 2 to n = 1
B. n = 3 to n = 2
C. n = 4 to n = 3
43
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Quantum Mechanics
Quantum Mechanics
How does quantum
mechanics differ from
classical mechanics?
44
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Quantum Mechanics
Given that light behaves as waves and
particles, can particles of matter behave as
waves?
• Louis de Broglie referred to the wavelike
behavior of particles as matter waves.
• His reasoning led him to a mathematical
expression for the wavelength of a moving
particle.
45
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Quantum Mechanics
The Wavelike Nature of Matter
Today, the wavelike properties of beams of
electrons are useful in viewing objects that cannot
be viewed with an optical microscope.
• The electrons in an electron
microscope have much smaller
wavelengths than visible light.
• These smaller wavelengths allow a
much clearer enlarged image of a
very small object, such as this pollen
grain, than is possible with an
ordinary microscope.
46
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Quantum Mechanics
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.
47
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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.
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Quantum Mechanics
• 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.
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After collision:
The impact
changes the
electron’s velocity,
making it
uncertain.
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The Heisenberg uncertainty principle
states that it is impossible to
simultaneously know which two
attributes of a particle?
velocity
and
position
__________________________
50
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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.
51
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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 = 
E=h
52
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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
53
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5.3 Atomic Emission Spectra and
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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
54
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5.3 Atomic Emission Spectra and
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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
()
• photoelectric effect: the phenomenon in
which electrons are ejected when light
shines on a metal
55
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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
56
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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.
57
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END OF 5.3
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