Chapter 27

1. Chapter 27 Quantum Physics Conceptual questions: 1,3,9,10 Quick Quizzes: 1,2,3 Problems: 13,42,43,51

2. Problems which classical physics could not solve • Blackbody Radiation • E&M radiation emitted by a heated object • Photoelectric Effect • Emission of electrons by an illuminated metal • X-Ray Diffraction • The Compton Effect • Spectral Lines Emitted by Atoms

3. Blackbody Radiation • An object at any temperature is known to emit electromagnetic radiation, called thermal radiation • Stefan’s Law, the power radiated by an object, P = s A e T4 • T-temperature, A-area, e-emissivity, s=5.669 10-8 W/m2 K4 • The spectrum of the radiation depends on the temperature and properties of the object

4. Blackbody Radiation Graph • The wavelength of the peak of the blackbody distribution was found to follow Wein’s Displacement Law • λmax T = 0.2898 x 10-2 m • K • λmax is the wavelength at the curve’s peak

5. The Ultraviolet Catastrophe and Planck’s theory • Classical theory predicted infinite energy at low wavelengths • Planck hypothesized that the blackbody radiation was produced by resonators • The resonators could only have discrete energies • En = n h ƒ • n is called the quantum number • ƒ is the frequency of vibration • h is Planck’s constant, 6.626 x 10-34 J s

6. Photoelectric Effect • When light strikes E, photoelectrons are emitted • Electrons collected at C and passing through the ammeter are a current in the circuit • C is maintained at a positive potential by the power supply

7. Photoelectric Current/Voltage Graph Classical theory could not explain: • The stopping potential is independent of the radiation intensity • The maximum kinetic energy of the photoelectrons is independent of the light intensity • The maximum kinetic energy of the photoelectrons increases with increasing light frequency

8. Einstein’s Explanation • Light is a collection of photons (not waves) • The photon’s energy would be E = hƒ • E=nhf-(n-1)hf • Each photon can give all its energy to an electron in the metal • The maximum kinetic energy of the liberated photoelectron is KE = hƒ – Φ • Φ is called the work function of the metal

9. Verification of Einstein’s Theory Problem 27-13. What wavelength of light would have to fall on sodium (work function 2.46 eV) if it is to emit electrons with a maximum speed of 1.0 x 106 m/s?

10. Photocells • Photocells are an application of the photoelectric effect • When light of sufficiently high frequency falls on the cell, a current is produced • Examples • Streetlights, garage door openers, elevators

11. Problem 27-13 • What wavelength of light would have to fall on sodium(with a work function of 2.46 eV) if it is to emit electronswith a maximum speed of 1.0 × 106 m/s?

12. X-Rays • Electromagnetic radiation with short wavelengths • Wavelengths less than for ultraviolet • Wavelengths are typically about 0.1 nm • X-rays have the ability to penetrate most materials with relative ease • Discovered and named by Roentgen in 1895

13. Production of X-rays

14. Schematic for X-ray Diffraction • A continuous beam of X-rays is incident on the crystal • The diffracted radiation is very intense in certain directions • These directions correspond to constructive interference from waves reflected from the layers of the crystal

15. Diffraction pattern for NaCl

16. Bragg’s Law • Bragg’s Law gives the conditions for constructive interference 2 d sin θ = m λ m = 1, 2, 3…

17. Compton Scattering • Compton assumed the photons acted like other particles in collisions • Energy and momentum were conserved • The shift in wavelength is

18. QUICK QUIZ 27.1 An x-ray photon is scattered by an electron. The frequency of the scattered photon relative to that of the incident photon (a) increases, (b) decreases,(c) remains the same.

19. QUICK QUIZ 27.2 A photon of energy E0 strikes a free electron, with the scattered photon of energy E moving in the direction opposite that of the incident photon. In this Compton effect interaction, the resulting kinetic energy of the electron is (a) E0 , (b) E , (c) E0 E ,(d) E0 + E , (e) none of the above.

20. Photons and Electromagnetic Waves • Light has a dual nature. It exhibits both wave and particle characteristics • Applies to all electromagnetic radiation • The photoelectric effect and Compton scattering offer evidence for the particle nature of light • Interference and diffraction offer evidence of the wave nature of light

21. Wave Properties of Particles • In 1924, Louis de Broglie postulated that because photons have wave and particle characteristics, perhaps all forms of matter have both properties • Furthermore, the frequency and wavelength of matter waves can be determined

22. de Broglie Wavelength and Frequency • The de Broglie wavelength of a particle is • The frequency of matter waves is

23. QUICK QUIZ 27.3 A non-relativistic electron and a non-relativistic proton are moving and have the same de Broglie wavelength. Which of the following are also the same for the two particles: (a) speed, (b) kinetic energy, (c) momentum, (d) frequency?

24. The Electron Microscope • The electron microscope depends on the wave characteristics of electrons • Microscopes can only resolve details that are slightly smaller than the wavelength of the radiation used to illuminate the object • The electrons can be accelerated to high energies and have small wavelengths

25. The Uncertainty Principle • When measurements are made, the experimenter is always faced with experimental uncertainties in the measurements • Classical mechanics would allow for measurements with arbitrarily small uncertainties • Quantum mechanics predicts that a barrier to measurements with ultimately small uncertainties does exist

26. Heisenberg’s Uncertainty Principle • Mathematically, • It is physically impossible to measure simultaneously the exact position and the exact linear momentum of a particle • Another form of the principle deals with energy and time:

27. Problem 27-43 In the ground state of hydrogen, the uncertainty of the position of the electron is roughly 0.10 nm. If the speed of the electron is on the order of the uncertainty in its speed, how fast is the electron moving?

28. Thought Experiment – the Uncertainty Principle • A thought experiment for viewing an electron with a powerful microscope • In order to see the electron, at least one photon must bounce off it • During this interaction, momentum is transferred from the photon to the electron • Therefore, the light that allows you to accurately locate the electron changes the momentum of the electron

29. Scanning Tunneling Microscope (STM) • Allows highly detailed images with resolution comparable to the size of a single atom • A conducting probe with a sharp tip is brought near the surface • The electrons can “tunnel” across the barrier of empty space

30. Conceptual questions • 1. If you observe objects inside a very hot kiln, it is difficult to discern the shapes of the objects. Why? • 3. Are the blackbodies really black? • 9. In the photoelectric effect, explain why the stopping potential depends on the frequency of the light but not on the intensity. • 10. Which has more energy, a photon of ultraviolet radiation or a photon of yellow light?

31. Problems • 42. A 50-g ball moves at 30.0 m/s. If its speed is measured to an accuracy of 0.10%, what is the minimum uncertainty in its position? • 51. Photons of wavelength 450 nm are incident on a metal. The most energetic electrons ejected from the metal are bent into a circular arc of radius 20.0 cm by a magnetic field with a magnitude of 2.00 × 10–5 T. What is the work function of the metal?