Lecture 36 Chapter 31 Light Quanta Matter Waves Uncertainty Principle

Transcription

1 Lecture 36 Chapter 31 Light Quanta Matter Waves Uncertainty Principle 24-Nov-10 Birth of Quantum Theory There has been a long historical debate about the nature of light: Some believed it to be particle-like. Others believed it to be wave-like. Young s double-slit interference experiment in 1801 proved that light had wave aspects. Emission of photons of light from atomic transitions suggested particle-like aspects Max Planck in 1900 hypothesized that radiant energy was emitted in discrete bundles, each of which he called a quantum. (Now called photon)

2 Quantization and Planck s Constant Quantum physics states that in the microworld of the atom, the amount of energy in any system is quantized not all values of energy are possible. Example: The energy in a beam of laser light, which is a whole-number multiple of a single lowest value of energy one quantum The quanta of light, and of electromagnetic radiation in general, are photons. Energy of a photon of frequency f: E = hf where h is Planck s constant h = 6.6 x J/Hz or 6.6 x J s Note: Value of h on text p. 549 is wrong! Quantization Quantization The idea that physical variables (energy, speed, momentum) are granular rather than smoothly continuous. Values must change in minimumsized steps. Quantum The step size, or smallest amount of change in the value of a physical variable. Example: The quantum of energy for a set of red photons (frequency f) is the energy of one photon, E = h f, where h is Planck s constant.

3 The Photon Model A model for how matter radiates EM waves Hypothesized by Max Planck, a German theoretical physicist in early 1900s Warm bodies emit radiant energy (light) in individualized bundles (quanta) -- photons. Energy in each photon is proportional to the frequency of radiation. E ~ f, or with Planck s constant h, E = hf Example What is the energy of a photon of frequency 3 x Hz? (h = 6.6 x J/Hz)

4 Example What is the energy of a photon of frequency 3 x Hz? (h = 6.6 x J/Hz) E = hf = (6.6 x J/Hz)(3 x Hz) = 2.0 x J The Photoelectric Effect Light shining on a metal surface can liberate electrons. The liberated electrons are attracted to the positive plate and produce a measurable current. If we instead put a large enough negative voltage on the plate, the current can be stopped. We can then calculate the energies of the ejected electrons from the easily measured potential difference between the plates.

5 The Photoelectric Effect The photoelectric effect (continued) The Photoelectric Effect The photoelectric effect (continued)

6 The Photoelectric Effect Einstein s view on light interactions Light (and all EM waves) are emitted and received as a stream of particles; bundles of energy (photons). Photons interact with matter one at a time. High-energy photons dislodge electrons from certain metals. The Photoelectric Effect CHECK YOURSELF In the photoelectric effect, the brighter the illuminating light on a photosensitive surface, the greater the A. velocity of ejected electrons. B. number of ejected electrons per second C. Both A and B. D. None of the above.

7 The Photoelectric Effect CHECK YOUR ANSWER In the photoelectric effect, the brighter the illuminating light on a photosensitive surface, the greater the A. velocity of ejected electrons. B. number of ejected electrons per second. C. Both A and B. D. None of the above. The Photoelectric Effect CHECK YOURSELF In the photoelectric effect, the higher the frequency of the illuminating light on a photosensitive surface, the greater the A. velocity of ejected electrons. B. number of ejected electrons per second. C. Both A and B. D. None of the above.

8 The Photoelectric Effect CHECK YOUR ANSWER In the photoelectric effect, the higher the frequency of the illuminating light on a photosensitive surface, the greater the A. velocity of ejected electrons. B. number of ejected electrons per second. C. Both A and B. D. None of the above. Wave Particle Duality Wave particle duality A photon behaves as a particle when emitted by an atom or absorbed by photographic film or other detectors. But it behaves as a wave in traveling from a source to the place where it is detected. In this sense, light can be both a wave and a particle!

9 Wave Particle Duality Wave particle duality (continued) This image is built up photon by photon. Double-Slit Experiment Double-slit experiment Monochromatic light passing through two slits forms an interference pattern.

10 Double-Slit Experiment with Photons Suppose we dim our light source so that only one photon at a time reaches the barrier with thin slits. If film behind the barrier is exposed to the light for a very short time, the film gets exposed as shown below. Each spot represents the place where the film has been hit by a photon. If the light is allowed to expose the film for a longer time, a pattern of fringes begins to emerge Double-Slit Experiment & Photons If we cover one slit so that photons striking the photographic film can pass only through a single slit, the tiny spots on the film accumulate to form a single-slit diffraction pattern. We find that photons hit the film at places they would not hit if both slits were open.

11 Double-Slit Experiment How do photons traveling through one slit know that the other slit is open and avoid certain regions, proceeding only to areas that will ultimately fill to form an interference pattern? Each single photon has wave properties as well as particle properties. The photon displays different aspects at different times. A photon behaves as a particle when it is being emitted by an atom or absorbed by photographic film or other detectors, and behaves as a wave in traveling from a source to the place where it is detected. So, the photon strikes the film as a particle but travels to its position as a wave that can interfere with other waves. Particles as Waves: Electron Diffraction Particles as waves: electron diffraction Every particle of matter is associated with a corresponding wave. According to de Broglie, a particle s wavelength is related to its momentum. where h is Planck s constant. (h = 6.6 x J s) Wavelength = h momentum λ = h/p

12 Particles as Waves: Electron Diffraction CHECK YOURSELF When we speak of de Broglie waves, we re speaking of the wave nature of A. light. B. sound. C. massive particles. D. quantum uncertainties. Particles as Waves: Electron Diffraction CHECK YOUR ANSWER When we speak of de Broglie waves, we re speaking of the wave nature of A. light. B. sound. C. massive particles. D. quantum uncertainties.

13 Example What is the de Broglie wavelength of a particle of mass 1 x kg moving at a speed of 6.6 x 10 5 m/s? (h = 6.6 x J s) Example What is the de Broglie wavelength of a particle of mass 1 x kg moving at a speed of 6.6 x 10 5 m/s? (h = 6.6 x J s) λ = h/p = h/(mv) = (6.6 x J s)/[(1 x kg)(6.6 x 10 5 m/s)] = 1 x m

14 Particles as Waves: Electron Diffraction Interference patterns of beams of light (left) and electrons (right) compared Particles as Waves: Electron Diffraction Electron microscope uses the wave nature of electrons to create images similar to the image of the mosquito shown here.

15 Uncertainty Principle Uncertainty principle The act of observing something as tiny as an electron disturbs the electron and, in so doing, produces a considerable uncertainty in either its position or its motion. Uncertainty Principle Uncertainty principle (continued) German physicist Werner Heisenberg called this the uncertainty principle. When the uncertainties p and x in measurements of momentum p and position x for a particle are multiplied together, the product must be equal to or greater than Planck s constant, h, divided by 2π, which is represented h as ( h-bar ). p x h

16 Uncertainty Principle Uncertainty principle (continued) The is uncertainty in measurement of : p is uncertainty in measurement of p and x the uncertainty in position. The product of uncertainties must be equal to or greater than ( ) the size of. h Uncertainty Principle Uncertainty principle (continued) Applies also to uncertainties of measurements of energy and time. The uncertainty in knowledge of energy, E, and the duration taken to measure the energy, t, are related by the expression: E t. h

17 Uncertainty Principle CHECK YOURSELF To which of these does Heisenberg s uncertainty principle apply? A. Measuring room temperature with a thermometer B. Momentum and distances of a high-speed bullet C. A public opinion survey D. None of the above. Uncertainty Principle CHECK YOUR ANSWER To which of these does Heisenberg s uncertainty principle apply? A. Measuring room temperature with a thermometer B. Momentum and distances of a high-speed bullet C. A public opinion survey D. None of the above. Explanation: Heisenberg s uncertainty principle involves the unavoidable interaction between nature at the atomic level and the means by which we probe it.

18 Complementarity Complementarity Wholeness often means accepting alternate explanations for natural phenomena. Opposite ideas can complement one another (light can be both a wave and a particle). Bohr chose the yin-yang diagram to illustrate complementarity. Key Points of Lecture 36 Birth of Quantum Theory Quantization and Planck s Constant Photon Energy Photoelectric Effect Wave Particle Duality Double-Slit Experiment - Quantum View Particles as Waves: de Broglie wavelength Uncertainty Principle Complementarity Before Wednesday Dec. 1, read Hewitt Chap. 30. Homework #24 due by 11:00 PM Monday Nov. 29 Homework #25 due by 11:00 PM Friday Dec. 3