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5.3 Atomic Emission Spectra and
the Quantum Mechanical 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
5.3 Atomic Emission Spectra and
the Quantum Mechanical Model
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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.
CHEMISTRY & YOU
5.3 Atomic Emission Spectra and
the Quantum Mechanical Model
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Light and Atomic
Emission Spectra
Light and Atomic Emission Spectra
What causes atomic emission
spectra?
5.3 Atomic Emission Spectra and
the Quantum Mechanical Model
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The Nature of Light
• 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
(the Greek letter lambda), is the
distance between the crests.
Light and Atomic
Emission Spectra
5.3 Atomic Emission Spectra and
the Quantum Mechanical Model
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• 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).
Light and Atomic
Emission Spectra
The Nature of Light
5.3 Atomic Emission Spectra and
the Quantum Mechanical Model
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The product of frequency and wavelength
equals a constant (c), the speed of light.
c =
Light and Atomic
Emission Spectra
The Nature of Light
5.3 Atomic Emission Spectra and
the Quantum Mechanical Model
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The frequency () and wavelength () of
light are inversely proportional to each
other. As the wavelength increases, the
frequency decreases.
Light and Atomic
Emission Spectra
5.3 Atomic Emission Spectra and
the Quantum Mechanical Model
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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.
Light and Atomic
Emission Spectra
The Nature of Light
5.3 Atomic Emission Spectra and
the Quantum Mechanical Model
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The sun and incandescent light bulbs emit white
light, which consists of light with a continuous
range of wavelengths and frequencies.
Light and Atomic
Emission Spectra
The Nature of Light
• 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.
5.3 Atomic Emission Spectra and
the Quantum Mechanical Model
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The electromagnetic spectrum consists of
radiation over a broad range of wavelengths.
Light and Atomic
Emission Spectra
Wavelength (m)
Low energy
( = 700 nm) High energy
( = 380 nm)
Frequency (s-1)
3 x 106 3 x 1012 3 x 1022
102 10-8 10-14
5.3 Atomic Emission Spectra and
the Quantum Mechanical Model
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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.
Light and Atomic
Emission Spectra
Atomic Emission Spectra
5.3 Atomic Emission Spectra and
the Quantum Mechanical Model
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A prism separates light into the colors it
contains. White light produces a rainbow
of colors.
Light and Atomic
Emission Spectra
Light
bulb
Slit Prism
Screen
Atomic Emission Spectra
5.3 Atomic Emission Spectra and
the Quantum Mechanical Model
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Light from a helium lamp produces
discrete lines.
Light and Atomic
Emission Spectra
Slit Prism
Screen
Helium
lamp
Atomic Emission Spectra
5.3 Atomic Emission Spectra and
the Quantum Mechanical Model
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• The energy absorbed by an electron for it to move
from its current energy level to a higher energy level
is identical to 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.
• No two elements have the same emission spectrum.
Light and Atomic
Emission Spectra
Atomic Emission Spectra
5.3 Atomic Emission Spectra and
the Quantum Mechanical Model
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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).
5.3 Atomic Emission Spectra and
the Quantum Mechanical Model
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Sample Problem 5.2
Use the equation c = to solve for the
unknown wavelength.
KNOWNS frequency () = 5.09 × 1014 /s
c = 2.998 × 108 m/s
UNKNOWN
wavelength () = ? m
Analyze List the knowns and the unknown. 1
5.3 Atomic Emission Spectra and
the Quantum Mechanical Model
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Sample Problem 5.2
Write the expression that relates the
frequency and wavelength of light.
c =
Calculate Solve for the unknown. 2
5.3 Atomic Emission Spectra and
the Quantum Mechanical Model
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Sample Problem 5.2
Rearrange the equation to solve for .
= c
Solve for by dividing
both sides by :
= c
Calculate Solve for the unknown. 2
c =
5.3 Atomic Emission Spectra and
the Quantum Mechanical Model
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Sample Problem 5.2
Substitute the known values for and c into
the equation and solve.
= = = 5.89 10–7 m c 2.998 108 m/s
5.09 1014 /s
Calculate Solve for the unknown. 2
5.3 Atomic Emission Spectra and
the Quantum Mechanical Model
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Sample Problem 5.2
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.
Evaluate Does the answer make sense? 3
5.3 Atomic Emission Spectra and
the Quantum Mechanical Model
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What is the frequency of a red laser
that has a wavelength of 676 nm?
5.3 Atomic Emission Spectra and
the Quantum Mechanical Model
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What is the frequency of a red laser
that has a wavelength of 676 nm?
c =
= = = 4.43 1014 m c 2.998 108 m/s 6.76 10–7 /s
c
=
5.3 Atomic Emission Spectra and
the Quantum Mechanical Model
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How did Einstein explain the
photoelectric effect?
The Quantum Concept and Photons
The Quantum Concept
and Photons
5.3 Atomic Emission Spectra and
the Quantum Mechanical Model
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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 ().
The Quantization of Energy
E or E = h
The Quantum Concept
and Photons
5.3 Atomic Emission Spectra and
the Quantum Mechanical Model
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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.
The Quantization of Energy
The Quantum Concept
and Photons
E or E = h
5.3 Atomic Emission Spectra and
the Quantum Mechanical Model
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Albert Einstein used Planck’s quantum theory
to explain the photoelectric effect.
The Photoelectric Effect
In the photoelectric effect, electrons
are ejected when light shines on a
metal.
The Quantum Concept
and Photons
5.3 Atomic Emission Spectra and
the Quantum Mechanical Model
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Not just any frequency of light will cause the
photoelectric effect.
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.
The Quantum Concept
and Photons
5.3 Atomic Emission Spectra and
the Quantum Mechanical Model
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• 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.
The Photoelectric Effect
The Quantum Concept
and Photons
5.3 Atomic Emission Spectra and
the Quantum Mechanical Model
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To explain the photoelectric effect,
Einstein proposed that light could be
described as quanta of energy that
behave as if they were particles.
The Photoelectric Effect
The Quantum Concept
and Photons
5.3 Atomic Emission Spectra and
the Quantum Mechanical Model
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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.
The Quantum Concept
and Photons
The Photoelectric Effect
5.3 Atomic Emission Spectra and
the Quantum Mechanical Model
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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
wavelike and particle-like properties.
5.3 Atomic Emission Spectra and
the Quantum Mechanical Model
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The Quantum Concept
and Photons
No electrons are ejected
because the frequency
of the light is below the
threshold frequency.
If the light is at or above
the threshold frequency,
electrons are ejected.
If the frequency is
increased, the ejected
electrons will travel
faster.
The Photoelectric Effect
5.3 Atomic Emission Spectra and
the Quantum Mechanical Model
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Calculating the Energy of a Photon
What is the energy of
a photon of
microwave radiation
with a frequency of
3.20 × 1011/s?
Sample Problem 5.3
5.3 Atomic Emission Spectra and
the Quantum Mechanical Model
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Sample Problem 5.3
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
Analyze List the knowns and the unknown. 1
5.3 Atomic Emission Spectra and
the Quantum Mechanical Model
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Sample Problem 5.3
Write the expression that relates the
energy of a photon of radiation and the
frequency of the radiation.
E = h
Calculate Solve for the unknown. 2
5.3 Atomic Emission Spectra and
the Quantum Mechanical Model
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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
Sample Problem 5.3
Calculate Solve for the unknown. 2
5.3 Atomic Emission Spectra and
the Quantum Mechanical Model
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Sample Problem 5.3
Individual photons have very small
energies, so the answer seems
reasonable.
Evaluate Does the result make sense? 3
5.3 Atomic Emission Spectra and
the Quantum Mechanical Model
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What is the frequency of a photon
whose energy is 1.166 10–17 J?
5.3 Atomic Emission Spectra and
the Quantum Mechanical Model
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What is the frequency of a photon
whose energy is 1.166 10–17 J?
E = h
= h E
= = = 1.760 1016 Hz E 6.626 10–34 J h 1.166 10–17 J·s
5.3 Atomic Emission Spectra and
the Quantum Mechanical Model
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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?
5.3 Atomic Emission Spectra and
the Quantum Mechanical Model
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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.
5.3 Atomic Emission Spectra and
the Quantum Mechanical Model
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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.
5.3 Atomic Emission Spectra and
the Quantum Mechanical Model
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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.
5.3 Atomic Emission Spectra and
the Quantum Mechanical Model
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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.
5.3 Atomic Emission Spectra and
the Quantum Mechanical Model
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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?
CHEMISTRY & YOU
5.3 Atomic Emission Spectra and
the Quantum Mechanical Model
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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.
CHEMISTRY & YOU
5.3 Atomic Emission Spectra and
the Quantum Mechanical Model
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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
5.3 Atomic Emission Spectra and
the Quantum Mechanical Model
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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
5.3 Atomic Emission Spectra and
the Quantum Mechanical Model
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Quantum Mechanics
Quantum Mechanics
How does quantum mechanics
differ from classical mechanics?
5.3 Atomic Emission Spectra and
the Quantum Mechanical Model
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Given that light behaves as waves and
particles, can particles of matter behave as
waves?
Quantum Mechanics
5.3 Atomic Emission Spectra and
the Quantum Mechanical Model
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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.
Quantum Mechanics
5.3 Atomic Emission Spectra and
the Quantum Mechanical Model
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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.
Quantum Mechanics
5.3 Atomic Emission Spectra and
the Quantum Mechanical Model
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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.
Quantum Mechanics
5.3 Atomic Emission Spectra and
the Quantum Mechanical Model
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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.
Quantum Mechanics
5.3 Atomic Emission Spectra and
the Quantum Mechanical Model
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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.
Quantum Mechanics
5.3 Atomic Emission Spectra and
the Quantum Mechanical Model
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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.
Quantum Mechanics
5.3 Atomic Emission Spectra and
the Quantum Mechanical Model
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• 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.
Quantum Mechanics
Before collision:
A photon strikes
an electron
during an attempt
to observe the
electron’s
position.
After collision:
The impact
changes the
electron’s velocity,
making it
uncertain.
5.3 Atomic Emission Spectra and
the Quantum Mechanical Model
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The Heisenberg uncertainty principle
states that it is impossible to
simultaneously know which two
attributes of a particle?
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the Quantum Mechanical Model
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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
5.3 Atomic Emission Spectra and
the Quantum Mechanical Model
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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.
Key Concepts and
Key Equations
5.3 Atomic Emission Spectra and
the Quantum Mechanical Model
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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
Key Concepts and
Key Equations
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the Quantum Mechanical Model
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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
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the Quantum Mechanical Model
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• 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
Glossary Terms
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the Quantum Mechanical Model
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• 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
Glossary Terms
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the Quantum Mechanical Model
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• 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
Glossary Terms
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the Quantum Mechanical Model
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Electrons and the Structure of Atoms
BIG IDEA
• 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.
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the Quantum Mechanical Model
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END OF 5.3