Electrons in Atoms
Chapter 5
Light and Quantized Energy
Section 5.1
Objectives
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Compare the wave and particle models of
light.
Define a quantum of energy and explain how
it is related to an energy change of matter.
Contrast continuous electromagnetic spectra
and atomic emission spectra.
Recall . . .

Rutherford’s nuclear
atomic model
–
–
All of an atom’s positive
charge and almost all of
its mass are concentrated
in a central structure
called the nucleus.
Fast-moving electrons are
found in the space
surrounding the nucleus.
Unanswered Questions

Rutherford’s atomic model was incomplete.
–
–
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Why weren’t the negatively charged electrons pulled
into the positively charged nucleus?
How were electrons “arranged” around the nucleus?
How does the model explain differences in chemical
behavior between elements?
More Unanswered Questions

Copper
Fluorine

In the early 1900’s,
scientists found that certain
elements emitted visible
light when heated in a
flame. Different elements
emitted different colors of
light.
Analysis of the emitted light
revealed that this chemical
behavior is related to the
arrangement of electrons in
an element’s atoms.
Understanding the Nature of Light

Wave Nature of Light
–
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Electromagnetic radiation is a form of energy that
exhibits wavelike behavior as it travels through
space.
Different types of EM radiation include radio
waves, microwaves, X rays, and visible light
(also called sunlight or white light).
All forms of EM radiation can be depicted in an
electromagnetic spectrum. See pg. 139 in text.
The Electromagnetic Spectrum
Wave Characteristics
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Notice (from the EM spectrum) that each
type of radiation has a characteristic
wavelength and frequency.
Wavelength and frequency, along with
amplitude and speed, are 4 characteristics
common to all waves.
Wave Characteristics


Wavelength,
represented by the
symbol λ (lambda), is the
length of 1 wave. It is
defined as the distance
between equivalent
points on a continuous
wave.
Generally, wavelength is
measured crest to crest
or trough to trough.
Wave Characteristics

Wavelength (cont.)
–
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The units for wavelength
are units of distance - m,
cm, or nm.
Amplitude is the height
of a wave from its origin
to its crest (or trough).
Wave Characteristics

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Frequency, represented by the symbol ν (nu) or ƒ,
is the number of waves that pass a given point in a
unit of time.
Hertz (Hz), the SI unit for frequency, equals 1
wave per second.
In calculations, frequency is expressed with the
units “waves per second” where “waves” is
accepted as understood. Frequency is in 1/s or
s-1.
82 Hz = 82 waves/second = 82/s = 82 s-1
Wave Characteristics
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All electromagnetic waves travel at a speed of
3.00 x 108 m/s in a vacuum. This is often
referred to as “the speed of light” even though
it refers to all EM waves.
The symbol for the speed of light is c.
Mathematically, the speed of light is the
product of its wavelength and its frequency or
C = λf
C = λf
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Wavelength and frequency
are inversely proportional.
This means, that if the
wavelength increases, the
frequency has to decrease
(and vice versa).
If a type of EM radiation has
a long wavelength, its
frequency must low. If it
has a short wavelength, its
frequency is high.
Practice Problems
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What is the frequency of green light, which has
a wavelength of 4.90 x 10-7 m?
An x ray has a wavelength of 1.15 x 10-10m.
What is its frequency?
What is the speed of an electromagnetic wave
that has a frequency of 7.8 x 106 Hz?
What is the wavelength of a microwave having
a frequency of 3.44 x 109 Hz?
White Light
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Let’s look closer at sunlight. Remember, it is a
type of EM radiation.
Sunlight (and all EM radiation) contains a
continuous range of wavelengths and
frequencies.
A prism will separate white light into a
continuous spectrum of colors.
The colors of the visible spectrum are
ROYGBIV.
White Light
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The visible spectrum (as
well as the EM
spectrum) is a
continuous spectrum
because every part of it
corresponds to a unique
λ and ν.
Each color then
corresponds to a
particular wavelength &
frequency.
White Light
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Red light has a relatively long λ and low frequency
while violet light has a short λ and a high
frequency.
Energy increases with frequency. Therefore violet
light has more energy than red light (or yellow or
green).
Wave Model of Light

Much evidence supports the idea that light, or any EM
radiation, is a form of energy that travels through
space as a wave. This is the “wave model" of light.

This model does not explain all of light’s characteristics:
– Why do hot objects emit only certain frequencies of
light? (see Fig. 6 p. 141)
– Why do certain metals emit electrons when certain
colors of light hit them (called the photoelectric
effect)? (see Fig. 7 p. 142)
– Why do elements emit distinctive colors of light when
burned?
The Particle Nature of light

Max Planck (1858-1947) searched for an
explanation for the color of light emitted from
heated objects.
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The temperature of an object is a measure of the
average kinetic energy of its particles.
As an object got hotter, it emitted different colors of
light.
Different colors correspond to different wavelengths
and, therefore, different frequencies of light.
Quantum/Quanta
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Max Planck concluded that matter can gain
energy only in small, specific amounts called
quanta. A quantum is the minimum amount of
energy that can be gained or lost by an atom.
Therefore, objects increase in temperature in
small steps as they absorb quanta of energy
The steps are so small the temperature
increase seems continuous.
An Analogy
Quanta
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4

3
2
1
0
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Think of each quantum of
energy as a step in a
staircase.
To walk up the staircase,
you move up one step at a
time. You do not move up
a 1/2 step or 1 1/2 steps.
When an object increases
in energy, it increases 1
quantum at a time.
The Particle Nature of Light
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Planck said the light energy emitted by hot
objects is quantized - it is emitted in quantum
units of energy.
He showed that the energy emitted is related
to the frequency of the light through this
equation: Equantum = hf
–
–
h is called Planck’s constant and is equal to
6.626 x 10-34 J-s (J stands for joule)
f is the frequency in s-1
E = hf
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This equation shows that matter can emit or
absorb energy only in whole number multiples
of hf - quantities of energy between these
values does not exist.
This equation could explain the photoelectric
effect as well as the color changes of objects
as they heat up.
–
The photoelectric effect is when electrons are
emitted from a metal’s surface when light of a
certain frequency shines on it.
The Photoelectric Effect
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According to the wave model, any color light should cause
the emission of “photoelectrons” from a metallic surface.
It was observed, however, that the light had to be of a
minimum frequency (or higher) to cause the photoelectric
effect.
The Particle Nature of light
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In 1905, Albert Einstein combined Planck’s
idea of quantized energy with the wave nature
of light and proposed the Dual Theory of
Light.
He proposed that light is composed of tiny
bundles of energy (called photons) that
behave like particles but travel in waves.
A photon is a particle of EM radiation with no
mass that carries one quantum of energy.
Photons
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Einstein said that a photon’s energy would
depend on its frequency. He modified Planck’s
equation: Ephoton = hf
Einstein proposed that there is a minimum or
threshold frequency that a photon of light must
have to cause ejection of photoelectrons.
Photons below that frequency would not have
enough energy to cause photoelectron ejection.
–
High frequency violet light causes electron emission
while red light does not.
(E = hf
Practice Problems
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h = 6.626 x 10-34 J-s)
What is the energy of a photon of violet light
that has a frequency of 7.23 x 1014 s-1?
What is the frequency of a photon of EM
radiation that has 6.29 x 10-20 J of energy?
What is the energy of EM radiation having a
frequency of 1.05 x 1016 s-1?
Atomic Emission Spectra
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The light of a neon sign is produced by passing
electricity through a tube filled with neon gas.
Neon atoms absorb energy and become
excited. They are unstable.
Unstable atoms release the energy as light (to
stabilize themselves.)
If the light emitted is passed through a prism, a
series of colored lines are produced. See Fig.
8, p. 144
Atomic Emission Spectra
Atomic Emission Spectra
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The atomic emission spectrum of an element
is the set of frequencies of the
electromagnetic waves emitted by atoms of
the element.
An AES consists of individual lines of color - it
is NOT continuous.
An AES is also referred to as a bright line or
line spectra.
Atomic Emission Spectra
Each atom has a unique AES. (see next slide)
 The elements of an unknown compound can
be identified by using the AES of
known elements.
 A flame test is a large scale
version of an AES and is used
as a quick way to make
identifications.

Fluorine
Hydrogen
Mercury
Helium
Atomic Emission Spectra
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The fact that only certain colors appear (as
lines) in an element’s spectrum means that
only certain specific frequencies of light are
emitted.
Those frequencies can be related to energy by
the formula: Ephoton = hv.
The conclusion is that only photons having
certain specific energies are emitted from
“excited” atoms.
Photons