1. Introduction to Quantum Physics
Chapter 40
Introduction to
Quantum Physics

2. Need for Quantum Physics
Problems remained from classical mechanics that relativity didn’t explain
Attempts to apply the laws of classical physics to explain the behavior of matter on the atomic scale were consistently unsuccessful
Problems included:
Blackbody radiation
The electromagnetic radiation emitted by a heated object
Photoelectric effect
Emission of electrons by an illuminated metal

3. Quantum Mechanics Revolution
Between 1900 and 1930, another revolution took place in physics
A new theory called quantum mechanics was successful in explaining the behavior of particles of microscopic size
The first explanation using quantum theory was introduced by Max Planck
Many other physicists were involved in other subsequent developments

4. Blackbody Radiation
An object at any temperature is known to emit thermal radiation
Characteristics depend on the temperature and surface properties
The thermal radiation consists of a continuous distribution of wavelengths from all portions of the em spectrum

5. Blackbody Radiation, cont.
At room temperature, the wavelengths of the thermal radiation are mainly in the infrared region
As the surface temperature increases, the wavelength changes
It will glow red and eventually white
The basic problem was in understanding the observed distribution in the radiation emitted by a black body
Classical physics didn’t adequately describe the observed distribution

6. Blackbody Radiation, final
A black body is an ideal system that absorbs all radiation incident on it
The electromagnetic radiation emitted by a black body is called blackbody radiation

7. Blackbody Approximation
A good approximation of a black body is a small hole leading to the inside of a hollow object
The hole acts as a perfect absorber
The nature of the radiation leaving the cavity through the hole depends only on the temperature of the cavity

8. Blackbody Experiment Results
The total power of the emitted radiation increases with temperature
Stefan’s law (from Chapter 20):
 = sAeT4
The peak of the wavelength distribution shifts to shorter wavelengths as the temperature increases
Wien’s displacement law
lmaxT = x 10-3 m.K

9. Intensity of Blackbody Radiation, Summary
The intensity increases with increasing temperature
The amount of radiation emitted increases with increasing temperature
The area under the curve
The peak wavelength decreases with increasing temperature

10. Active Figure 40.3
Use the active figure to adjust the temperature of the blackbody
Study the emitted radiation
PLAY
ACTIVE FIGURE

11. Rayleigh-Jeans Law
An early classical attempt to explain blackbody radiation was the Rayleigh-Jeans law
At long wavelengths, the law matched experimental results fairly well

12. Rayleigh-Jeans Law, cont.
At short wavelengths, there was a major disagreement between the Rayleigh-Jeans law and experiment
This mismatch became known as the ultraviolet catastrophe
You would have infinite energy as the wavelength approaches zero

13. Max Planck 1858 – 1847 German physicist
Introduced the concept of “quantum of action”
In 1918 he was awarded the Nobel Prize for the discovery of the quantized nature of energy

14. Planck’s Theory of Blackbody Radiation
In 1900 Planck developed a theory of blackbody radiation that leads to an equation for the intensity of the radiation
This equation is in complete agreement with experimental observations
He assumed the cavity radiation came from atomic oscillations in the cavity walls
Planck made two assumptions about the nature of the oscillators in the cavity walls

15. Planck’s Assumption, 1
The energy of an oscillator can have only certain discrete values En
En = nhƒ
n is a positive integer called the quantum number
ƒ is the frequency of oscillation
h is Planck’s constant
This says the energy is quantized
Each discrete energy value corresponds to a different quantum state

16. Planck’s Assumption, 2
The oscillators emit or absorb energy when making a transition from one quantum state to another
The entire energy difference between the initial and final states in the transition is emitted or absorbed as a single quantum of radiation
An oscillator emits or absorbs energy only when it changes quantum states
The energy carried by the quantum of radiation is E = h ƒ

17. Energy-Level Diagram
An energy-level diagram shows the quantized energy levels and allowed transitions
Energy is on the vertical axis
Horizontal lines represent the allowed energy levels
The double-headed arrows indicate allowed transitions

18. More About Planck’s Model
The average energy of a wave is the average energy difference between levels of the oscillator, weighted according to the probability of the wave being emitted
This weighting is described by the Boltzmann distribution law and gives the probability of a state being occupied as being proportional to
where E is the energy of the state

19. Planck’s Model, Graph

20. Active Figure 40.7
Use the active figure to investigate the energy levels
Observe the emission of radiation of different wavelengths
PLAY
ACTIVE FIGURE

21. Planck’s Wavelength Distribution Function
Planck generated a theoretical expression for the wavelength distribution
h = x J.s
h is a fundamental constant of nature

22. Planck’s Wavelength Distribution Function, cont.
At long wavelengths, Planck’s equation reduces to the Rayleigh-Jeans expression
At short wavelengths, it predicts an exponential decrease in intensity with decreasing wavelength
This is in agreement with experimental results

23. Photoelectric Effect
The photoelectric effect occurs when light incident on certain metallic surfaces causes electrons to be emitted from those surfaces
The emitted electrons are called photoelectrons

24. Photoelectric Effect Apparatus
When the tube is kept in the dark, the ammeter reads zero
When plate E is illuminated by light having an appropriate wavelength, a current is detected by the ammeter
The current arises from photoelectrons emitted from the negative plate and collected at the positive plate

25. Active Figure 40.9
Use the active figure to vary frequency or place voltage
Observe the motion of the electrons
PLAY
ACTIVE FIGURE

26. Photoelectric Effect, Results
At large values of DV, the current reaches a maximum value
All the electrons emitted at E are collected at C
The maximum current increases as the intensity of the incident light increases
When DV is negative, the current drops
When DV is equal to or more negative than DVs, the current is zero

27. Active Figure 40.10 Use the active figure to change the voltage range
Observe the current curve for different intensities of radiation

28. Photoelectric Effect Feature 1
Dependence of photoelectron kinetic energy on light intensity
Classical Prediction
Electrons should absorb energy continually from the electromagnetic waves
As the light intensity incident on the metal is increased, the electrons should be ejected with more kinetic energy
Experimental Result
The maximum kinetic energy is independent of light intensity
The maximum kinetic energy is proportional to the stopping potential (DVs)

29. Photoelectric Effect Feature 2
Time interval between incidence of light and ejection of photoelectrons
Classical Prediction
At low light intensities, a measurable time interval should pass between the instant the light is turned on and the time an electron is ejected from the metal
This time interval is required for the electron to absorb the incident radiation before it acquires enough energy to escape from the metal
Experimental Result
Electrons are emitted almost instantaneously, even at very low light intensities

30. Photoelectric Effect Feature 3
Dependence of ejection of electrons on light frequency
Classical Prediction
Electrons should be ejected at any frequency as long as the light intensity is high enough
Experimental Result
No electrons are emitted if the incident light falls below some cutoff frequency, ƒc
The cutoff frequency is characteristic of the material being illuminated
No electrons are ejected below the cutoff frequency regardless of intensity

31. Photoelectric Effect Feature 4
Dependence of photoelectron kinetic energy on light frequency
Classical Prediction
There should be no relationship between the frequency of the light and the electric kinetic energy
The kinetic energy should be related to the intensity of the light
Experimental Result
The maximum kinetic energy of the photoelectrons increases with increasing light frequency

32. Photoelectric Effect Features, Summary
The experimental results contradict all four classical predictions
Einstein extended Planck’s concept of quantization to electromagnetic waves
All electromagnetic radiation can be considered a stream of quanta, now called photons
A photon of incident light gives all its energy hƒ to a single electron in the metal

33. Photoelectric Effect, Work Function
Electrons ejected from the surface of the metal and not making collisions with other metal atoms before escaping possess the maximum kinetic energy Kmax
Kmax = hƒ – φ
φ is called the work function
The work function represents the minimum energy with which an electron is bound in the metal

34. Some Work Function Values

35. Photon Model Explanation of the Photoelectric Effect
Dependence of photoelectron kinetic energy on light intensity
Kmax is independent of light intensity
K depends on the light frequency and the work function
Time interval between incidence of light and ejection of the photoelectron
Each photon can have enough energy to eject an electron immediately

36. Photon Model Explanation of the Photoelectric Effect, cont.
Dependence of ejection of electrons on light frequency
There is a failure to observe photoelectric effect below a certain cutoff frequency, which indicates the photon must have more energy than the work function in order to eject an electron
Without enough energy, an electron cannot be ejected, regardless of the light intensity

37. Photon Model Explanation of the Photoelectric Effect, final
Dependence of photoelectron kinetic energy on light frequency
Since Kmax = hƒ – φ
As the frequency increases, the kinetic energy will increase
Once the energy of the work function is exceeded
There is a linear relationship between the kinetic energy and the frequency

38. Cutoff Frequency
The lines show the linear relationship between K and ƒ
The slope of each line is h
The x-intercept is the cutoff frequency
This is the frequency below which no photoelectrons are emitted

39. Cutoff Frequency and Wavelength
The cutoff frequency is related to the work function through ƒc = φ / h
The cutoff frequency corresponds to a cutoff wavelength
Wavelengths greater than lc incident on a material having a work function φ do not result in the emission of photoelectrons

40. Arthur Holly Compton 1892 – 1962 American physicist
Director of the lab at the University of Chicago
Discovered the Compton Effect
Shared the Nobel Prize in 1927

41. The Compton Effect, Introduction
Compton and Debye extended with Einstein’s idea of photon momentum
The two groups of experimenters accumulated evidence of the inadequacy of the classical wave theory
The classical wave theory of light failed to explain the scattering of x-rays from electrons

42. Compton Effect, Classical Predictions
According to the classical theory, em waves incident on electrons should:
Have radiation pressure that should cause the electrons to accelerate
Set the electrons oscillating
There should be a range of frequencies for the scattered electrons

43. Compton Effect, Observations
Compton’s experiments showed that, at any given angle, only one frequency of radiation is observed

44. Compton Effect, Explanation
The results could be explained by treating the photons as point-like particles having energy hƒ
Assume the energy and momentum of the isolated system of the colliding photon-electron are conserved
This scattering phenomena is known as the Compton effect

45. Compton Shift Equation
The graphs show the scattered x-ray for various angles
The shifted peak, λ’ is caused by the scattering of free electrons
This is called the Compton shift equation

46. Compton Wavelength
The factor h/mec in the equation is called the Compton wavelength and is
The unshifted wavelength, λo, is caused by x-rays scattered from the electrons that are tightly bound to the target atoms

47. Photons and Waves Revisited
Some experiments are best explained by the photon model
Some are best explained by the wave model
We must accept both models and admit that the true nature of light is not describable in terms of any single classical model
Also, the particle model and the wave model of light complement each other

48. Louis de Broglie 1892 – 1987 French physicist
Originally studied history
Was awarded the Nobel Prize in 1929 for his prediction of the wave nature of electrons

49. Wave Properties of Particles
Louis de Broglie postulated that because photons have both wave and particle characteristics, perhaps all forms of matter have both properties
The de Broglie wavelength of a particle is

50. Frequency of a Particle
In an analogy with photons, de Broglie postulated that a particle would also have a frequency associated with it
These equations present the dual nature of matter
Particle nature, p and E
Wave nature, λ and ƒ

51. Davisson-Germer Experiment
If particles have a wave nature, then under the correct conditions, they should exhibit diffraction effects
Davisson and Germer measured the wavelength of electrons
This provided experimental confirmation of the matter waves proposed by de Broglie

52. Complementarity
The principle of complementarity states that the wave and particle models of either matter or radiation complement each other
Neither model can be used exclusively to describe matter or radiation adequately

53. Electron Microscope
The electron microscope relies on the wave characteristics of electrons
The electron microscope has a high resolving power because it has a very short wavelength
Typically, the wavelengths of the electrons are about 100 times shorter than that of visible light

54. Quantum Particle
The quantum particle is a new model that is a result of the recognition of the dual nature
Entities have both particle and wave characteristics
We must choose one appropriate behavior in order to understand a particular phenomenon

55. Ideal Particle vs. Ideal Wave
An ideal particle has zero size
Therefore, it is localized in space
An ideal wave has a single frequency and is infinitely long
Therefore,it is unlocalized in space
A localized entity can be built from infinitely long waves

56. Particle as a Wave Packet
Multiple waves are superimposed so that one of its crests is at x = 0
The result is that all the waves add constructively at x = 0
There is destructive interference at every point except x = 0
The small region of constructive interference is called a wave packet
The wave packet can be identified as a particle

57. Active Figure 40.19
Use the active figure to choose the number of waves to add together
Observe the resulting wave packet
The wave packet represents a particle
PLAY
ACTIVE FIGURE

58. Wave Envelope The blue line represents the envelope function
This envelope can travel through space with a different speed than the individual waves

59. Active Figure 40.20
Use the active figure to observe the movement of the waves and of the wave envelope
PLAY
ACTIVE FIGURE

60. Speeds Associated with Wave Packet
The phase speed of a wave in a wave packet is given by
This is the rate of advance of a crest on a single wave
The group speed is given by
This is the speed of the wave packet itself

61. Speeds, cont.
The group speed can also be expressed in terms of energy and momentum
This indicates that the group speed of the wave packet is identical to the speed of the particle that it is modeled to represent

62. Electron Diffraction, Set-Up

63. Electron Diffraction, Experiment
Parallel beams of mono-energetic electrons that are incident on a double slit
The slit widths are small compared to the electron wavelength
An electron detector is positioned far from the slits at a distance much greater than the slit separation

64. Electron Diffraction, cont.
If the detector collects electrons for a long enough time, a typical wave interference pattern is produced
This is distinct evidence that electrons are interfering, a wave-like behavior
The interference pattern becomes clearer as the number of electrons reaching the screen increases

65. Active Figure 40.22
Use the active figure to observe the development of the interference pattern
Observe the destruction of the pattern when you keep track of which slit an electron goes through
Please replace with active figure 40.22
PLAY
ACTIVE FIGURE

66. Electron Diffraction, Equations
A maximum occurs when
This is the same equation that was used for light
This shows the dual nature of the electron
The electrons are detected as particles at a localized spot at some instant of time
The probability of arrival at that spot is determined by finding the intensity of two interfering waves

67. Electron Diffraction Explained
An electron interacts with both slits simultaneously
If an attempt is made to determine experimentally which slit the electron goes through, the act of measuring destroys the interference pattern
It is impossible to determine which slit the electron goes through
In effect, the electron goes through both slits
The wave components of the electron are present at both slits at the same time

68. Werner Heisenberg 1901 – 1976 German physicist
Developed matrix mechanics
Many contributions include:
Uncertainty principle
Rec’d Nobel Prize in 1932
Prediction of two forms of molecular hydrogen
Theoretical models of the nucleus

69. The Uncertainty Principle, Introduction
In classical mechanics, it is possible, in principle, to make measurements with arbitrarily small uncertainty
Quantum theory predicts that it is fundamentally impossible to make simultaneous measurements of a particle’s position and momentum with infinite accuracy

70. Heisenberg Uncertainty Principle, Statement
The Heisenberg uncertainty principle states: if a measurement of the position of a particle is made with uncertainty Dx and a simultaneous measurement of its x component of momentum is made with uncertainty Dpx, the product of the two uncertainties can never be smaller than /2

71. Heisenberg Uncertainty Principle, Explained
It is physically impossible to measure simultaneously the exact position and exact momentum of a particle
The inescapable uncertainties do not arise from imperfections in practical measuring instruments
The uncertainties arise from the quantum structure of matter

72. Heisenberg Uncertainty Principle, Another Form
Another form of the uncertainty principle can be expressed in terms of energy and time
This suggests that energy conservation can appear to be violated by an amount DE as long as it is only for a short time interval Dt