1 Chapter 29 Particles and Waves

2 There is nothing new to be discovered in physics now. All that remains is more and more precise measurement. -- William Thomson, Lord Kelvin (Address at the British Association for the Advancement of Science, 1900).

3 Quantum Physics 2nd revolution in physics: –Starts with Planck ~1900 –Contributions from Einstein, Bohr, Heisenberg, Schrödinger, Born, Dirac, de Broglie …. over 25 years Cornerstones: –Wave-particle duality –Uncertainty principle Correspondence –Applies for small dimensions Planck’s constant: h = 6.6 x Js As h -> 0, quantum physics -> classical

4 Front row: I. Langmuir, M. Planck, M. Curie, H. A. Lorentz, A. Einstein, P. Langevin, C. E. Guye, C. T. R. Wilson, O. W. Richardson. Second row: P. Debye, M. Knudsen, W. L. Bragg, H. A. Kramers, P. A. M. Dirac, A. H. Compton, L. V. de Broglie, M. Born, N. Bohr. Standing: A. Piccard, E. Henriot, P. Ehrenfest, E. Herzen, T. De Donder, E. Schroedinger, E. Verschaffelt, W. Pauli, W. Heisenberg, R. H. Fowler, L. Brillouin. Solvay conference, 1927

5 Front row: I. Langmuir, M. Planck, M. Curie, H. A. Lorentz, A. Einstein, P. Langevin, C. E. Guye, C. T. R. Wilson, O. W. Richardson. Second row: P. Debye, M. Knudsen, W. L. Bragg, H. A. Kramers, P. A. M. Dirac, A. H. Compton, L. V. de Broglie, M. Born, N. Bohr. Standing: A. Piccard, E. Henriot, P. Ehrenfest, E. Herzen, T. De Donder, E. Schroedinger, E. Verschaffelt, W. Pauli, W. Heisenberg, R. H. Fowler, L. Brillouin. Planck Curie Lorentz Bragg Einstein Dirac Compton de Broglie Born Bohr Schr ö dinger Heisenberg Pauli Solvay conference, 1927

6 Part I: Particle nature of light

7 1. Blackbody radiation All objects radiate and absorb electromagnetic radiation At equilibrium, rate of absorption = rate of emission Best absorber is best emitter –Perfect absorber is perfect emitter Cavity is model of a perfect blackbody a) Blackbody

8 Plot of intensity vs wavelength –Depends only on temperature b) Emmitance spectrum: the problem Experimental spectrum:

9 Classical prediction: The UV catastrophe Theory Based on idea that all oscillations equally probable, more oscillations at lower wavelength Violates common sense and experiment

10 Absorption and emission occur in discrete quanta only c) Energy quantization: the solution Energy of quanta proportional to frequency For small wavelength (high freq), quanta are large. If kT < quantum, radiation not possible.

11 Planck found a “fudge factor” by “happy guesswork” to make the experiment fit. He developed a quantization theory to predict the value h. –“lucky artifact of more fundamental reality yet to be discovered” d) Planck’s constant, h Nobel prize, 1918

12 2. Photoelectric effect a) The effect

13 ExperimentExpectationObservation Increase intensity - Max energy increase - Current increase - Time lag decrease - Max energy constant - Current increase - No time lag Increase Frequency - Max energy constant - No threshold b) Expectations and observations

14 Observed frequency dependence

15 ExperimentExpectationObservation Increase intensity - Max energy increase - Current increase - Time lag decrease - Max energy constant - Current increase - No time lag Increase Frequency - Max energy constant - No threshold - Max energy prop to freq - Threshold frequency characteristic of metal b) Expectations and observations

16 KE max = hf - W 0 Energy of photon (from Planck) Work required to remove electron c) Einstein theory

17 Found same value for h as Planck had Nobel prize in 1921 In 1913, Planck recommended Einstein for membership in the Prussian Academy. “Notwithstanding his genius, he may sometimes have missed the target in his speculations, as, for example, in his hypothesis of light quanta.”

18 a)The effect: Scattering of x-ray by electron changes the wavelength 3. The Compton Effect, 1923

19 b) The experiment  Crystal X-ray source ( ) Bragg reflection gives ’ graphite Detector

20 c) Classical prediction - incident wave excites electron at frequency f - electron radiates at frequency f

21 d) Compton’s explanation - Conservation of Momentum: - Energy-momentum relation for light: - Conservation of energy: Combining these equations gives: ’ Nobel prize, 1928 Definitive evidence for photons

22 Part II: The wave nature of particles

23 a)The hypothesis 4. The de Broglie wavelength, 1924 The dual nature observed in light is present in matter: By analogy, de Broglie proposed that a particle with momentum p is associated with a wave with wavelength: A photon has energy From electromagnetism, }

24 b) Electron diffraction/interference

25 b) Interpretation of the particle wave Waves and particles propogate and interfere like waves, but interact like particles. The intensity of the wave (represented by a wave function  at a point in space represents the probability of observing a particle at that location.

26 5. The Heisenberg Uncertainty Principle The wave nature of particles means that position and momentum (wavelength) cannot simultaneously be determined to arbitrary accuracy. The smaller the slit above, the better the y-position is known, but the greater the spread in y-momentum.

27 The principle applies separately to any component of momentum and position: and to energy and time: