1. 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. 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

5. 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

6. Photoelectric Effect, Results At large values of  V, 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  V is negative, the current drops When  V is equal to or more negative than  V s, the current is zero

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

8. 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 (  V s )

9. 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

10. 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, ƒ c The cutoff frequency is characteristic of the material being illuminated No electrons are ejected below the cutoff frequency regardless of intensity

11. 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

12. 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

13. 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 K max K max = hƒ – φ φ is called the work function The work function represents the minimum energy with which an electron is bound in the metal

14. Some Work Function Values

15. Photon Model Explanation of the Photoelectric Effect Dependence of photoelectron kinetic energy on light intensity K max 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

16. 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

17. Photon Model Explanation of the Photoelectric Effect, final Dependence of photoelectron kinetic energy on light frequency Since K max = 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

18. 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

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

20. 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

21. 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

22. 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

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

24. 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

25. 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

26. Compton Wavelength The factor h/m e c in the equation is called the Compton wavelength and is The unshifted wavelength, λ o, is caused by x- rays scattered from the electrons that are tightly bound to the target atoms

27. 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

28. 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

29. 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

30. 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

31. 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

32. 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

33. Electron Diffraction, Set-Up

34. 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

35. 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

36. 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

37. 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

38. 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

39. 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

40. 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

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

42. 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

43. 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  E as long as it is only for a short time interval  t