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= 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 = 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, x 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 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 electrons with 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?