Preview

1
Chapter 21
Section 1 Quantization of Energy
Preview

• Objectives
• Blackbody Radiation
• Quantum Energy
• The Photoelectric Effect
• Compton Shift

2
Objectives
Section 1 Quantization of Energy
Chapter 21

• Explain how Planck resolved the ultraviolet
  catastrophe in blackbody radiation.
• Calculate energy of quanta using Plancks
  equation.
• Solve problems involving maximum kinetic energy,
  work function, and threshold frequency in the
  photoelectric effect.

3
Blackbody Radiation
Section 1 Quantization of Energy
Chapter 21

• Physicists study blackbody radiation by observing
  a hollow object with a small opening, as shown in
  the diagram.

• A blackbody is a perfect radiator and absorber
  and emits radiation based only on its
  temperature.

Light enters this hollow object through the
small opening and strikes the interior wall. Some
of the energy is absorbed, but some is reflected
at a random angle. After many reflections,
essentially all of the incoming energy is
absorbed by the cavity wall.
4
Blackbody Radiation, continued
Chapter 21
Section 1 Quantization of Energy

• The ultraviolet catastrophe is the failed
  prediction of classical physics that the energy
  radiated by a blackbody at extremely short
  wavelengths is extremely large and that the total
  energy radiated is infinite.
• Max Planck (18581947) developed a formula for
  blackbody radiation that was in complete
  agreement with experimental data at all
  wavelengths by assuming that energy comes in
  discrete units, or is quantized.

5
Blackbody Radiation
Chapter 21
Section 1 Quantization of Energy
The graph on the left shows the intensity of
blackbody radiation at three different
temperatures. Classical theorys prediction for
blackbody radiation (the blue curve) did not
correspond to the experimental data (the red data
points) at all wavelengths, whereas Plancks
theory (the red curve) did.
6
Blackbody Radiation and the Ultraviolet
Catastrophe
Chapter 21
Section 1 Quantization of Energy
Click below to watch the Visual Concept.
Visual Concept
7
Quantum Energy
Chapter 21
Section 1 Quantization of Energy

• Einstein later applied the concept of quantized
  energy to light. The units of light energy called
  quanta (now called photons) are absorbed or given
  off as a result of electrons jumping from one
  quantum state to another.

• The energy of a light quantum, which corresponds
  to the energy difference between two adjacent
  levels, is given by the following equation

E hf energy of a quantum Plancks constant ?
frequency Plancks constant (h) 6.63 ? 1034
Js
8
Quantum Energy
Chapter 21
Section 1 Quantization of Energy

• If Plancks constant is expressed in units of
  Js, the equation E hf gives the energy in
  joules.
• However, in atomic physics, energy is often
  expressed in units of the electron volt, eV.
• An electron volt is defined as the energy that an
  electron or proton gains when it is accelerated
  through a potential difference of 1 V.
• The relation between the electron volt and the
  joule is as follows
• 1 eV 1.60 ? 1019 J

9
Energy of a Photon
Chapter 21
Section 1 Quantization of Energy
Click below to watch the Visual Concept.
Visual Concept
10
The Photoelectric Effect
Chapter 21
Section 1 Quantization of Energy

• The photoelectric effect is the emission of
  electrons from a material surface that occurs
  when light of certain frequencies shines on the
  surface of the material.
• Classical physics cannot explain the
  photoelectric effect.
• Einstein assumed that an electromagnetic wave can
  be viewed as a stream of particles called
  photons. Photon theory accounts for observations
  of the photoelectric effect.

11
The Photoelectric Effect
Chapter 21
Section 1 Quantization of Energy
12
The Photoelectric Effect
Chapter 21
Section 1 Quantization of Energy
Click below to watch the Visual Concept.
Visual Concept
13
The Photoelectric Effect, continued
Chapter 21
Section 1 Quantization of Energy

• No electrons are emitted if the frequency of the
  incoming light falls below a certain frequency,
  called the threshold frequency (ft).
• The smallest amount of energy the electron must
  have to escape the surface of a metal is the work
  function of the metal.
• The work function is equal to hft.

14
The Photoelectric Effect, continued
Chapter 21
Section 1 Quantization of Energy

• Because energy must be conserved, the maximum
  kinetic energy (of photoelectrons ejected from
  the surface) is the difference between the photon
  energy and the work function of the metal.

maximum kinetic energy of a photoelectron KEmax
hf hft maximum kinetic energy (Plancks
constant ? frequency of incoming photon) work
function
15
Compton Shift
Chapter 21
Section 1 Quantization of Energy

• If light behaves like a particle, then photons
  should have momentum as well as energy both
  quantities should be conserved in elastic
  collisions.
• The American physicist Arthur Compton directed X
  rays toward a block of graphite to test this
  theory.
• He found that the scattered waves had less energy
  and longer wavelengths than the incoming waves,
  just as he had predicted.
• This change in wavelength, known as the Compton
  shift, supports Einsteins photon theory of light.

16
Compton Shift
Chapter 21
Section 1 Quantization of Energy
Click below to watch the Visual Concept.
Visual Concept
17
Chapter 21
Section 2 Models of the Atom
Preview

• Objectives
• Early Models of the Atom
• Atomic Spectra
• The Bohr Model of the Hydrogen Atom
• Sample Problem

18
Objectives
Section 2 Models of the Atom
Chapter 21

• Explain the strengths and weaknesses of
  Rutherfords model of the atom.
• Recognize that each element has a unique emission
  and absorption spectrum.
• Explain atomic spectra using Bohrs model of the
  atom.
• Interpret energy-level diagrams.

19
Early Models of the Atom
Section 2 Models of the Atom
Chapter 21

• The model of the atom in the days of Newton was
  that of a tiny, hard, indestructible sphere.
• The discovery of the electron in 1897 prompted J.
  J. Thomson (18561940) to suggest a new model of
  the atom.
• In Thomsons model, electrons are embedded in a
  spherical volume of positive charge like seeds in
  a watermelon.

20
Early Models of the Atom, continued
Section 2 Models of the Atom
Chapter 21

• Ernest Rutherford (18711937) later proved that
  Thomsons model could not be correct.
• In his experiment, a beam of positively charged
  alpha particles was projected against a thin
  metal foil.

• Most of the alpha particles passed through the
  foil. Some were deflected through very large
  angles.

21
Rutherfords Gold Foil Experiment
Chapter 21
Section 2 Models of the Atom
Click below to watch the Visual Concept.
Visual Concept
22
Early Models of the Atom, continued
Section 2 Models of the Atom
Chapter 21

• Rutherford concluded that all of the positive
  charge in an atom and most of the atoms mass are
  found in a region that is small compared to the
  size of the atom.
• He called this region the the nucleus of the
  atom.
• Any electrons in the atom were assumed to be in
  the relatively large volume outside the nucleus.

23
Early Models of the Atom, continued
Section 2 Models of the Atom
Chapter 21

• To explain why electrons were not pulled into the
  nucleus, Rutherford viewed the electrons as
  moving in orbits about the nucleus.

• However, accelerated charges should radiate
  electromagnetic waves, losing energy. This would
  lead to a rapid collapse of the atom.
• This difficulty led scientists to continue
  searching for a new model of the atom.

24
Atomic Spectra
Section 2 Models of the Atom
Chapter 21

• When the light given off by an atomic gas is
  passed through a prism, a series of distinct
  bright lines is seen. Each line corresponds to a
  different wavelength, or color.

• A diagram or graph that indicates the wavelengths
  of radiant energy that a substance emits is
  called an emission spectrum.
• Every element has a distinct emission spectrum.

25
Atomic Spectra, continued
Section 2 Models of the Atom
Chapter 21

• An element can also absorb light at specific
  wavelengths.
• The spectral lines corresponding to this process
  form what is known as an absorption spectrum.
• An absorption spectrum can be seen by passing
  light containing all wavelengths through a vapor
  of the element being analyzed.
• Each line in the absorption spectrum of a given
  element coincides with a line in the emission
  spectrum of that element.

26
Emission and Absorption Spectra of Hydrogen
Section 2 Models of the Atom
Chapter 21
27
The Bohr Model of the Hydrogen Atom
Section 2 Models of the Atom
Chapter 21

• In 1913, the Danish physicist Niels Bohr (1885
  1962) proposed a new model of the hydrogen atom
  that explained atomic spectra.
• In Bohrs model, only certain orbits are allowed.
  The electron is never found between these orbits
  instead, it is said to jump instantly from one
  orbit to another.
• In Bohrs model, transitions between stable
  orbits with different energy levels account for
  the discrete spectral lines.

28
The Bohr Model, continued
Section 2 Models of the Atom
Chapter 21

• When light of a continuous spectrum shines on the
  atom, only the photons whose energy (hf ) matches
  the energy separation between two levels can be
  absorbed by the atom.

• When this occurs, an electron jumps from a lower
  energy state to a higher energy state, which
  corresponds to an orbit farther from the nucleus.
  
• This is called an excited state. The absorbed
  photons account for the dark lines in the
  absorption spectrum.

29
The Bohr Model, continued
Section 2 Models of the Atom
Chapter 21

• Once an electron is in an excited state, there is
  a certain probability that it will jump back to a
  lower energy level by emitting a photon.
• This process is called spontaneous emission.

• The emitted photons are responsible for the
  bright lines in the emission spectrum.
• In both cases, there is a correlation between the
  size of an electrons jump and the energy of
  the photon.

30
The Bohr Model of the Atom
Chapter 21
Section 2 Models of the Atom
Click below to watch the Visual Concept.
Visual Concept
31
Sample Problem
Section 2 Models of the Atom
Chapter 21

• Interpreting Energy-Level Diagrams
• An electron in a hydrogen atom drops from energy
  level E4 to energy level E2. What is the
  frequency of the emitted photon, and which line
  in the emission spectrum corresponds to this
  event?

32
Sample Problem, continued
Section 2 Models of the Atom
Chapter 21

• Find the energy of the photon.
• The energy of the photon is equal to the change
  in the energy of the electron. The electrons
  initial energy level was E4, and the electrons
  final energy level was E2. Using the values from
  the energy-level diagram gives the following
• E Einitial Efinal E4 E2
• E (0.850 eV) (3.40 eV) 2.55 eV

33
Sample Problem, continued
Section 2 Models of the Atom
Chapter 21

• Tip Note that the energies for each energy level
  are negative. The reason is that the energy of an
  electron in an atom is defined with respect to
  the amount of work required to remove the
  electron from the atom. In some energy-level
  diagrams, the energy of E1 is defined as zero,
  and the higher energy levels are positive.
• In either case, the difference between a higher
  energy level and a lower one is always positive,
  indicating that the electron loses energy when it
  drops to a lower level.

34
Sample Problem, continued
Section 2 Models of the Atom
Chapter 21
2. Use Plancks equation to find the frequency.

• Tip Note that electron volts were converted
  to joules so that the units cancel properly.

35
Sample Problem, continued
Section 2 Models of the Atom
Chapter 21

1. Find the corresponding line in the emission
   spectrum.

Examination of the diagram shows that the
electrons jump from energy level E4 to energy
level E2 corresponds to Line 3 in the emission
spectrum.
36
Sample Problem, continued
Section 2 Models of the Atom
Chapter 21
4. Evaluate your answer. Line 3 is in the
visible part of the electromagnetic spectrum and
appears to be blue. The frequency f 6.15 ? 1014
Hz lies within the range of the visible spectrum
and is toward the violet end, so it is reasonable
that light of this frequency would be visible
blue light.
37
The Bohr Model, continued
Section 2 Models of the Atom
Chapter 21

• Bohrs model was not considered to be a complete
  picture of the structure of the atom.
• Bohr assumed that electrons do not radiate energy
  when they are in a stable orbit, but his model
  offered no explanation for this.
• Another problem with Bohrs model was that it
  could not explain why electrons always have
  certain stable orbits
• For these reasons, scientists continued to search
  for a new model of the atom.

38
Chapter 21
Section 3 Quantum Mechanics
Preview

• Objectives
• The Dual Nature of Light
• Matter Waves
• The Uncertainty Principle
• The Electron Cloud

39
Objectives
Section 3 Quantum Mechanics
Chapter 21

• Recognize the dual nature of light and matter.
• Calculate the de Broglie wavelength of matter
  waves.
• Distinguish between classical ideas of
  measurement and Heisenbergs uncertainty
  principle.
• Describe the quantum-mechanical picture of the
  atom, including the electron cloud and
  probability waves.

40
The Dual Nature of Light
Section 3 Quantum Mechanics
Chapter 21

• As seen earlier, there is considerable evidence
  for the photon theory of light. In this theory,
  all electromagnetic waves consist of photons,
  particle-like pulses that have energy and
  momentum.
• On the other hand, light and other
  electromagnetic waves exhibit interference and
  diffraction effects that are considered to be
  wave behaviors.
• So, which model is correct?

41
The Dual Nature of Light, continued
Section 3 Quantum Mechanics
Chapter 21

• Some experiments can be better explained or only
  explained by the photon concept, whereas others
  require a wave model.
• Most physicists accept both models and believe
  that the true nature of light is not describable
  in terms of a single classical picture.
• At one extreme, the electromagnetic wave
  description suits the overall interference
  pattern formed by a large number of photons.
• At the other extreme, the particle description is
  more suitable for dealing with highly energetic
  photons of very short wavelengths.

42
The Dual Nature of Light
Chapter 21
Section 3 Quantum Mechanics
Click below to watch the Visual Concept.
Visual Concept
43
Matter Waves
Section 3 Quantum Mechanics
Chapter 21

• In 1924, the French physicist Louis de Broglie
  (18921987) extended the wave-particle duality.
  De Broglie proposed that all forms of matter may
  have both wave properties and particle
  properties.
• Three years after de Broglies proposal, C. J.
  Davisson and L. Germer, of the United States,
  discovered that electrons can be diffracted by a
  single crystal of nickel. This important
  discovery provided the first experimental
  confirmation of de Broglies theory.

44
Matter Waves, continued
Section 3 Quantum Mechanics
Chapter 21

• The wavelength of a photon is equal to Plancks
  constant (h) divided by the photons momentum
  (p). De Broglie speculated that this relationship
  might also hold for matter waves, as follows

• As seen by this equation, the larger the momentum
  of an object, the smaller its wavelength.

45
Matter Waves, continued
Section 3 Quantum Mechanics
Chapter 21

• In an analogy with photons, de Broglie postulated
  that the frequency of a matter wave can be found
  with Plancks equation, as illustrated below

• The dual nature of matter suggested by de Broglie
  is quite apparent in the wavelength and frequency
  equations, both of which contain particle
  concepts (E and mv) and wave concepts (? and f).

46
Matter Waves, continued
Section 3 Quantum Mechanics
Chapter 21

• De Broglie saw a connection between his theory of
  matter waves and the stable orbits in the Bohr
  model.

• He assumed that an electron orbit would be stable
  only if it contained an integral (whole) number
  of electron wavelengths.

47
De Broglie and the Wave-Particle Nature of
Electrons
Chapter 21
Section 3 Quantum Mechanics
Click below to watch the Visual Concept.
Visual Concept
48
The Uncertainty Principle
Section 3 Quantum Mechanics
Chapter 21

• In 1927, Werner Heisenberg argued that it is
  fundamentally impossible to make simultaneous
  measurements of a particles position and
  momentum with infinite accuracy.
• In fact, the more we learn about a particles
  momentum, the less we know of its position, and
  the reverse is also true.
• This principle is known as Heisenbergs
  uncertainty principle.

49
The Uncertainty Principle
Chapter 21
Section 3 Quantum Mechanics
Click below to watch the Visual Concept.
Visual Concept
50
The Electron Cloud
Section 3 Quantum Mechanics
Chapter 21

• Quantum mechanics also predicts that the electron
  can be found in a spherical region surrounding
  the nucleus.
• This result is often interpreted by viewing the
  electron as a cloud surrounding the nucleus.
• Analysis of each of the energy levels of hydrogen
  reveals that the most probable electron location
  in each case is in agreement with each of the
  radii predicted by the Bohr theory.

51
The Electron Cloud, continued
Section 3 Quantum Mechanics
Chapter 21

• Because the electrons location cannot be
  precisely determined, it is useful to discuss the
  probability of finding the electron at different
  locations.
• The diagram shows the probability per unit
  distance of finding the electron at various
  distances from the nucleus in the ground state of
  hydrogen.