Material particles and light have both wave properties and particle properties.

1

• Material particles and light have both wave
  properties and particle properties.

2

• Atomic structure is revealed by analyzing light.
  Light has a dual nature, which in turn radically
  alters our understanding of the atomic world.

3
38.1 Models

• Through the centuries there have been two primary
  models of light the particle model and the wave
  model.

4
38.1 Models
Nobody knows what an atoms internal structure
looks like, for there is no way to see it with
our eyes. To visualize the processes that occur
in the subatomic realm, we construct models. The
planetary model in which electrons orbit the
nucleus was suggested by the Danish physicist
Niels Bohr in 1913. It is still useful for
understanding the emission of light.
5
38.1 Models
The planetary model has been replaced by a more
complex model in which the electrons are
represented as clouds.
6
38.1 Models
Models help us to understand processes that are
difficult to visualize. A useful model of the
atom must be consistent with a model for
light. Most of what we know about atoms we learn
from the light and other radiations they emit.
Most light comes from the motion of electrons
within the atom.
7
38.1 Models

• There have been two primary models of light the
  particle model and the wave model.
• Isaac Newton believed light was composed of tiny
  particles.
• Christian Huygens believed that light was a wave
  phenomenon.

8
38.1 Models
The wave model was reinforced when Thomas Young
demonstrated constructive and destructive
interference of light. Later, James Clerk
Maxwell proposed that light is an electromagnetic
wave. The wave model gained further support when
Heinrich Hertz produced radio waves that behaved
as Maxwell had predicted. In 1905, Albert
Einstein resurrected the particle theory of light.
9
38.1 Models
What are the two primary models of light?
10
38.2 Light Quanta

• The energy of a photon is directly proportional
  to the photons frequency.

11
38.2 Light Quanta
Einstein visualized particles of light as
concentrated bundles of electromagnetic energy.
Max Planck had proposed that atoms do not emit
and absorb light continuously, but do so in
little chunks. Each chunk was considered a
quantum, or a fundamental unit.
12
38.2 Light Quanta
Planck believed that light existed as continuous
waves, but that emission and absorption occurred
in quantum chunks. Einstein went further and
proposed that light itself is composed of quanta.
One quantum of light energy is now called a
photon.
13
38.2 Light Quanta
Matter is quantized, equal to some whole-number
multiple of the mass of a single atom. Electric
charge is quantized as a multiple of the charge
of a single electron. Other quantities such as
energy and angular momentum are quantized.
14
38.2 Light Quanta

• The energy in a light beam is quantized and comes
  in packets, or quanta only a whole number of
  quanta can exist.
• The quanta of electromagnetic radiation are the
  photons.
• Photons have no rest energy.
• They move at the speed of light so the total
  energy of a photon is the same as its kinetic
  energy.

15
38.2 Light Quanta

• The energy of a photon of light is proportional
  to its vibrational frequency.
• When the energy E of a photon is divided by its
  frequency f, the quantity that results is known
  as Plancks constant, h.
• This quantity is always the same, no matter what
  the frequency.
• The energy of every photon is therefore E hf.
• This equation gives the smallest amount of energy
  that can be converted to light of frequency f.

16
38.2 Light Quanta
How is the energy of a photon related to its
frequency?
17
38.3 The Photoelectric Effect

• The photoelectric effect suggests that light
  interacts with matter as a stream of
  particle-like photons.

18
38.3 The Photoelectric Effect
Einstein found support for his quantum theory of
light in the photoelectric effect. The
photoelectric effect is the ejection of electrons
from certain metals when light falls upon them.
These metals are said to be photosensitive.
19
38.3 The Photoelectric Effect

• Explanation of the Photoelectric Effect

• Energy from the light shining on a metal plate
  gives electrons bound in the metal enough energy
  to escape.
• High-frequency light, even from a dim source, is
  capable of ejecting electrons from a
  photosensitive metal surface.
• Low-frequency light, even from a very bright
  source, cannot dislodge electrons.
• Since bright light carries more energy than dim
  light, it was puzzling that dim blue light could
  dislodge electrons when bright red light could
  not.

20
38.3 The Photoelectric Effect

• Einstein explained the photoelectric effect in
  terms of photons.
• The absorption of a photon by an atom in the
  metal surface is an all-or-nothing process.
• Only one photon is absorbed by each electron
  ejected from the metal.
• The number of photons that hit the metal has
  nothing to do with whether a given electron will
  be ejected.
• If the energy in the photon is large enough, the
  electron will be ejected from the metal.

21
38.3 The Photoelectric Effect

• The intensity of light does not matter. From E
  hf, the critical factor is the frequency, or
  color, of the light.
• Each blue or violet light photon carries enough
  energy to free an electron from the metal.
• A few photons of blue or violet light can eject a
  few electrons. Many red or orange photons cannot
  eject a single electron.
• Only high-frequency photons have the energy
  needed to pull loose an electron.

22
38.3 The Photoelectric Effect

• Support for the Particle Model of Light

The energy of a wave is spread out along a broad
front. For the energy of a light wave to be
concentrated enough to eject a single electron
from a metal surface is unlikely. The
photoelectric effect suggests that light
interacts with matter as a stream of
particle-like photons.
23
38.3 The Photoelectric Effect
The number of photons in a light beam controls
the brightness of the whole beam. The frequency
of the light controls the energy of each
individual photon. Experimental verification of
Einsteins explanation was made 11 years later by
the American physicist Robert Millikan. Every
aspect of Einsteins interpretation was
confirmed, including the direct proportionality
of photon energy to frequency.
24
38.3 The Photoelectric Effect

• think!
• Will high-frequency light eject a greater number
  of electrons than low-frequency light?

25
38.3 The Photoelectric Effect

• think!
• Will high-frequency light eject a greater number
  of electrons than low-frequency light?
• Answer
• Not necessarily. The answer is yes if electrons
  are ejected by the high-frequency light but not
  by the low-frequency light, because its photons
  do not have enough energy. If the light of both
  frequencies can eject electrons, then the number
  of electrons ejected depends on the brightness of
  the light, not on its frequency.

26
38.3 The Photoelectric Effect
What does the photoelectric effect suggest about
the way light interacts with matter?
27
38.4 Waves as Particles

• Light behaves like waves when it travels in empty
  space, and like particles when it interacts with
  solid matter.

28
38.4 Waves as Particles
A photograph taken with exceedingly feeble light
provides a striking example of the particle
nature of light. The image progresses photon by
photon. Photons seem to strike the film in an
independent and random manner.
29
38.4 Waves as Particles
What causes light to behave like a wave? Like a
particle?
30
38.5 Particles as Waves

• De Broglie suggested that all matter could be
  viewed as having wave properties.

31
38.5 Particles as Waves
If waves can have particle properties, cannot
particles have wave properties? This question
was posed by the French physicist Louis de
Broglie and his answer later won the Nobel Prize
in physics. De Broglie suggested that all matter
could be viewed as having wave properties.
32
38.5 Particles as Waves
All particleselectrons, protons, atoms, marbles,
and even humanshave a wavelength where h is
Plancks constant.
33
38.5 Particles as Waves

• The wavelength of a particle is called the de
  Broglie wavelength.
• A particle of large mass and ordinary speed has
  too small a wavelength to be detected by
  conventional means.
• A tiny particlesuch as an electronmoving at
  typical speed has a detectable wavelength.

34
38.5 Particles as Waves
The wavelength of electrons is smaller than the
wavelength of visible light but large enough for
noticeable diffraction. A beam of electrons can
be diffracted and undergoes wave interference
under the same conditions that light does.
35
38.5 Particles as Waves
This image of lily pollen grains was taken with a
scanning electron microscope. Electron
microscopes make use of the wave nature of
electrons.
36
38.5 Particles as Waves
What did de Broglie suggest about all matter?
37
38.6 Electron Waves

• According to de Broglies theory of matter waves,
  electron orbits exist only where an electron wave
  closes in on itself in phase.

38
38.6 Electron Waves

• The planetary model of the atom was useful in
  explaining the atomic spectra of the elements and
  why elements emitted only certain frequencies of
  light.
• An electron has different amounts of energy when
  it is in different orbits around a nucleus.
• An electron is in a different energy level when
  it is in a different orbit.
• Electrons in an atom normally occupy the lowest
  energy levels available.

39
38.6 Electron Waves
In the Bohr model of the atom, the electron
orbits correspond to different energy levels.
40
38.6 Electron Waves

• Bohr Model Explanation of Atomic Spectra

• An electron can be boosted to a higher energy
  level.
• This occurs in gas discharge tubes such as neon
  signs.
• Electric current boosts electrons of the gas to
  higher energy levels.
• As the electrons return to lower levels, photons
  are emitted.
• The energy of a photon is exactly equal to the
  difference in the energy levels in the atom.

41
38.6 Electron Waves
The pattern of lines in the spectrum of an
element corresponds to electron transitions
between the energy levels of the atoms of that
element. By examining spectra, physicists were
able to determine the various energy levels in
the atom.
42
38.6 Electron Waves
Why were electrons at discrete distances from the
atomic nucleus? This was resolved by thinking of
the electron not as a particle whirling around
the nucleus but as a wave. According to de
Broglies theory of matter waves, electron orbits
exist only where an electron wave closes in on
itself in phase.
43
38.6 Electron Waves

• De Broglies Theory

• The electron wave reinforces constructively in
  each cycle, like the standing wave on a music
  string.
• The electron is visualized not as a particle
  located at some point in the atom.
• Its mass and charge are spread throughout a
  standing wave surrounding the nucleus.
• The wavelength of the electron wave must fit
  evenly into the circumferences of the orbits.

44
38.6 Electron Waves

• De Broglie suggested electrons have a wavelength.
  
• Electron orbits exist only when the circumference
  of the orbit is a whole-number multiple of the
  wavelength.

45
38.6 Electron Waves

• De Broglie suggested electrons have a wavelength.
  
• Electron orbits exist only when the circumference
  of the orbit is a whole-number multiple of the
  wavelength.
• When the wave does not close in on itself in
  phase, it undergoes destructive interference.

46
38.6 Electron Waves
The circumference of the innermost orbit,
according to this model, is equal to one
wavelength of the electron wave. The second
orbit has a circumference of two electron
wavelengths, the third three, and so on.
47
38.6 Electron Waves
Orbit circumferences are whole-number multiples
of the electron wavelengths, which differ for the
various elements. This results in discrete
energy levels, which characterize each element.
Since the circumferences of electron orbits are
discrete, the radii of these orbits, and hence
the energy levels, are also discrete.
48
38.6 Electron Waves
In this simplified version of de Broglies theory
of the atom, the waves are shown only in circular
paths around the nucleus. In an actual atom, the
standing waves make up spherical and ellipsoidal
shells rather than flat, circular ones.
49
38.6 Electron Waves
This explains why electrons do not spiral closer
and closer to the nucleus when photons are
emitted. Since an orbit is described by a
standing wave, the circumference of the smallest
orbit can be no smaller than one wavelength. In
the modern wave model of the atom, electron waves
also move in and out, toward and away from the
nucleus. The electron wave is in three
dimensions, an electron cloud.
50
38.6 Electron Waves
How did de Broglies theory of matter waves
describe electron orbits?
51
38.7 Relative Sizes of Atoms

• The radii of the electron orbits in the Bohr
  model of the atom are determined by the amount of
  electric charge in the nucleus.

52
38.7 Relative Sizes of Atoms
The single proton in the hydrogen atom holds one
negatively charged electron in an orbit at a
particular radius. In helium, the orbiting
electron would be pulled into a tighter orbit
with half its former radius since the electrical
attraction is doubled. This doesnt quite happen
because the double-positive charge in the nucleus
attracts and holds a second electron. The
negative charge of the second electron diminishes
the effect of the positive nucleus.
53
38.7 Relative Sizes of Atoms
This added electron makes the atom electrically
neutral. The two electrons assume an orbit
characteristic of helium. In a lithium atom, an
additional proton pulls the electrons into an
even closer orbit and holds a third electron in a
second orbit.
54
38.7 Relative Sizes of Atoms
As the nuclear charge increases, the inner orbits
shrink because of the stronger electrical
attraction to the nucleus. This means that the
heavier elements are not much larger in diameter
than the lighter elements. The diameter of the
uranium atom, for example, is only about three
hydrogen diameters, even though it is 238 times
more massive.
55
38.7 Relative Sizes of Atoms
Each element has a unique arrangement of electron
orbits. The radii of orbits for the sodium atom
are the same for all sodium atoms, but different
from the radii of orbits for other kinds of
atoms. Each element has its own distinct orbits.
56
38.7 Relative Sizes of Atoms
The Bohr model solved the mystery of the atomic
spectra of the elements. It accounted for X-rays
that were emitted when electrons made transitions
from outer orbits to innermost orbits. Bohr was
able to predict X-ray frequencies that were later
experimentally confirmed.
57
38.7 Relative Sizes of Atoms
Bohr calculated the ionization energy of the
hydrogen atomthe energy needed to knock the
electron out of the atom completely. This also
was verified by experiment. The model accounted
for the chemical properties of the elements and
predicted properties of hafnium, which led to its
discovery.
58
38.7 Relative Sizes of Atoms
Bohr was quick to point out that his model was to
be interpreted as a crude beginning. The picture
of electrons whirling like planets about the sun
was not to be taken literally. His discrete
orbits were conceptual representations of an atom
whose later description involved a wave
description.
59
38.7 Relative Sizes of Atoms

1. In the Bohr model, the electrons orbit the
   nucleus like planets going around the sun.

60
38.7 Relative Sizes of Atoms

1. In the Bohr model, the electrons orbit the
   nucleus like planets going around the sun.
2. According to de Broglies idea, a wave follows
   along an orbit.

61
38.7 Relative Sizes of Atoms

1. In the Bohr model, the electrons orbit the
   nucleus like planets going around the sun.
2. According to de Broglies idea, a wave follows
   along an orbit.
3. The wave modelelectrons are distributed in a
   cloud throughout the volume of the atom.

62
38.7 Relative Sizes of Atoms

• think!
• What fundamental force dictates the size of an
  atom?

63
38.7 Relative Sizes of Atoms

• think!
• What fundamental force dictates the size of an
  atom?
• Answer
• The electrical force.

64
38.7 Relative Sizes of Atoms
What determines the radii of the electron orbits
in the Bohr model of the atom?
65
38.8 Quantum Physics

• The subatomic interactions described by quantum
  mechanics are governed by laws of probability,
  not laws of certainty.

66
38.8 Quantum Physics
Physicists became convinced that the Newtonian
laws that work so well for large objects do not
apply to the microworld of the atom. In the
macroworld, the study of motion is called
mechanics, or sometimes classical mechanics. The
study of the motion of particles in the
microworld of atoms and nuclei is called quantum
mechanics. The branch of physics that is the
general study of the microworld of photons,
atoms, and nuclei is simply called quantum
physics.
67
38.8 Quantum Physics
There are fundamental uncertainties in the
measurements of the atomic domain. For the
measurement of macroscopic quantities, such as
the temperature of materials or the speeds of
light and sound, there is no limit to the
accuracy with which the experimenter can measure.
68
38.8 Quantum Physics
Subatomic measurements, such as the momentum and
position of an electron or the mass of an
extremely short-lived particle, are entirely
different. In this domain, the uncertainties in
many measurements are comparable to the
magnitudes of the quantities themselves. The
subatomic interactions described by quantum
mechanics are governed by laws of probability,
not laws of certainty.
69
38.8 Quantum Physics
What laws govern the interactions described by
quantum mechanics?
70
38.9 Predictability and Chaos

• Predictability in orderly systems, both Newtonian
  and quantum, depends on knowledge of initial
  conditions.

71
38.9 Predictability and Chaos
When we know the initial conditions of an orderly
system we can make predictions about it. Knowing
the initial conditions lets us state where a
planet will be after a certain time or where a
launched rocket will land. In the quantum
microworld, we give odds where an electron is
likely to be. We calculate the probability that a
radioactive particle will decay in a given time
interval.
72
38.9 Predictability and Chaos
Some systems, however, whether Newtonian or
quantum, are not orderlythey are inherently
unpredictable. These are called chaotic
systems. A feature of chaotic systems is that
slight differences in initial conditions result
in wildly different outcomes later.
73
38.9 Predictability and Chaos
Weather is chaotic. Small changes in one days
weather can produce big (and largely
unpredictable) changes a week later. This
barrier to good prediction first led the
scientist Edward Lorenz to ask, Does the flap of
a butterflys wings in Brazil set off a tornado
in Texas? Now we talk about the butterfly
effect when dealing with situations where very
small effects can amplify into very big effects.
74
38.9 Predictability and Chaos
What determines predictability in orderly
systems?
75
Assessment Questions

• A model of an atom is useful when it
• shows exactly what an atom looks like.
• magnifies what the eye cant see.
• helps to visualize processes that cannot be seen
  with our eyes.
• is shown only as the planetary model.

76
Assessment Questions

• A model of an atom is useful when it
• shows exactly what an atom looks like.
• magnifies what the eye cant see.
• helps to visualize processes that cannot be seen
  with our eyes.
• is shown only as the planetary model.
• Answer C

77
Assessment Questions

• In the equation E hf, f stands for the
• frequency of a photon with energy E.
• wavelength of a photon with energy E.
• Plancks constant with energy h.
• quantum of energy.

78
Assessment Questions

• In the equation E hf, f stands for the
• frequency of a photon with energy E.
• wavelength of a photon with energy E.
• Plancks constant with energy h.
• quantum of energy.
• Answer A

79
Assessment Questions

• Which of these photons is more likely to initiate
  the photoelectric effect?
• red
• green
• blue
• violet

80
Assessment Questions

• Which of these photons is more likely to initiate
  the photoelectric effect?
• red
• green
• blue
• violet
• Answer D

81
Assessment Questions

• Which of these best illustrates the dual nature
  of light?
• Light travels as a wave and interacts with solid
  matter like a particle.
• Light travels as a particle and interacts with
  solid matter like a wave.
• Light can interact in empty spaces as do
  particles, and travel around solid matter as do
  waves.
• Light does not have a dual nature.

82
Assessment Questions

• Which of these best illustrates the dual nature
  of light?
• Light travels as a wave and interacts with solid
  matter like a particle.
• Light travels as a particle and interacts with
  solid matter like a wave.
• Light can interact in empty spaces as do
  particles, and travel around solid matter as do
  waves.
• Light does not have a dual nature.
• Answer A

83
Assessment Questions

• The wavelength of a matter wave is
• directly proportional to its momentum.
• inversely proportional to its momentum.
• equal to its momentum.
• theoretical only.

84
Assessment Questions

• The wavelength of a matter wave is
• directly proportional to its momentum.
• inversely proportional to its momentum.
• equal to its momentum.
• theoretical only.
• Answer B

85
Assessment Questions

• The view of radii of electrons about the atomic
  nucleus is nicely understood by thinking of the
  electrons as
• standing waves.
• discrete particles.
• resonating vibrations.
• reflections.

86
Assessment Questions

• The view of radii of electrons about the atomic
  nucleus is nicely understood by thinking of the
  electrons as
• standing waves.
• discrete particles.
• resonating vibrations.
• reflections.
• Answer A

87
Assessment Questions

• The greater the number of protons in a nucleus,
  the
• larger the orbits of the outermost electron.
• tighter the orbits of all electrons.
• looser inner orbits become.
• more electrically neutral the atom becomes.

88
Assessment Questions

• The greater the number of protons in a nucleus,
  the
• larger the orbits of the outermost electron.
• tighter the orbits of all electrons.
• looser inner orbits become.
• more electrically neutral the atom becomes.
• Answer B

89
Assessment Questions

• Subatomic interactions described by quantum
  mechanics are governed by
• the same laws of classical physics.
• laws of certainty.
• laws of probability.
• exact measurements.

90
Assessment Questions

• Subatomic interactions described by quantum
  mechanics are governed by
• the same laws of classical physics.
• laws of certainty.
• laws of probability.
• exact measurements.
• Answer C

91
Assessment Questions

• A feature of chaotic systems is that small
  changes in initial conditions
• lead to small differences later.
• lead to big differences later.
• may lead to big differences later.
• have little or no relation to small or big
  differences later.

92
Assessment Questions

• A feature of chaotic systems is that small
  changes in initial conditions
• lead to small differences later.
• lead to big differences later.
• may lead to big differences later.
• have little or no relation to small or big
  differences later.
• Answer C