1. 3.1 Discovery of the X-Ray and the Electron 3.2Determination of Electron Charge 3.3Line Spectra 3.4Quantization 3.5Blackbody Radiation 3.6Photoelectric Effect 3.7X-Ray Production 3.8Compton Effect 3.9Pair Production and Annihilation Prelude to Quantum Theory CHAPTER 3 Prelude to Quantum Theory Problems due Wednesday Sept. 24 th : Chapter 3: 7, 9, 14, 15, 16, 18, 19, 24, 25, 26 Max Karl Ernst Ludwig Planck (1858-1947)

2. Photons also have momentum! Use our expression for the relativistic energy to find the momentum of a photon, which has no mass: Alternatively: Comet tails (other forces are small) Viking spacecraft (would've missed Mars by 15,000 km) Stellar interiors (resists gravity) When radiation pressure is important:

3. 3.8: Compton Effect When a photon enters matter, it can interact with one of the electrons. The laws of conservation of energy and momentum apply, as in any elastic collision between two particles. This yields the change in wavelength of the scattered photon, known as the Compton effect: Photons have energy and momentum: E p, p p E p ’, p p ’ E e, p e Read: section 3.4 Kane

4. 3.9: Pair Production and Annihilation In 1932, C. D. Anderson observed a positively charged electron (e + ) in cosmic radiation. This particle, called a positron, had been predicted to exist several years earlier by P. A. M. Dirac. A photon’s energy can be converted entirely into an electron and a positron in a process called pair production: Paul Dirac (1902 - 1984)

5. Pair Production in Empty Space Conservation of energy for pair production in empty space is: This yields a lower limit on the photon energy: The total energy for a particle is: This yields an upper limit on the photon energy: Momentum conservation yields: A contradiction! And hence the conversion of energy and momentum for pair production in empty space is impossible! So: h E+E+ EE

6. Pair Production in Matter In the presence of matter, the nucleus absorbs some energy and momentum. The photon energy required for pair production in the presence of matter is:

7. Pair Annihilation A positron passing through matter will likely annihilate with an electron. The electron and positron can form an atom-like configuration first, called positronium. Pair annihilation in empty space produces two photons to conserve momentum. Annihilation near a nucleus can result in a single photon.

8. Pair Annihilation Conservation of energy: Conservation of momentum: So the two photons will have the same frequency: The two photons from positronium annihilation will move in opposite directions with an energy:

9. 4.1The Atomic Models of Thomson and Rutherford 4.2Rutherford Scattering 4.3The Classic Atomic Model 4.4The Bohr Model of the Hydrogen Atom 4.5Successes & Failures of the Bohr Model 4.6Characteristic X-Ray Spectra and Atomic Number 4.7Atomic Excitation by Electrons Structure of the Atom CHAPTER 4 Structure of the Atom The opposite of a correct statement is a false statement. But the opposite of a profound truth may well be another profound truth. An expert is a person who has made all the mistakes that can be made in a very narrow field. Never express yourself more clearly than you are able to think. Prediction is very difficult, especially about the future. - Niels Bohr Niels Bohr (1885-1962)

10. Structure of the Atom Evidence in 1900 indicated that the atom was not a fundamental unit: 1) There seemed to be too many kinds of atoms, each belonging to a distinct chemical element (way more than earth, air, water, and fire!). 2) Atoms and electromagnetic phenomena were intimately related (magnetic materials; insulators vs. conductors; different emission spectra). 3) Elements combine with some elements but not with others, a characteristic that hinted at an internal atomic structure (valence). 4) The discoveries of radioactivity, x rays, and the electron (all seemed to involve atoms breaking apart in some way).

11. Knowledge of atoms in 1900 Electrons (discovered in 1897) carried the negative charge. Electrons were very light, even compared to the atom. Protons had not yet been discovered, but clearly positive charge had to be present to achieve charge neutrality.

12. In Thomson’s view, when the atom was heated, the electrons could vibrate about their equilibrium positions, thus producing electromagnetic radiation. Unfortunately, Thomson couldn’t explain spectra with this model. Thomson’s Atomic Model Thomson’s “plum-pudding” model of the atom had the positive charges spread uniformly throughout a sphere the size of the atom, with electrons embedded in the uniform background.

13. Experiments of Geiger and Marsden Rutherford, Geiger, and Marsden conceived a new technique for investigating the structure of matter by scattering  particles from atoms.

14. Experiments of Geiger and Marsden 2 Geiger showed that many  particles were scattered from thin gold-leaf targets at backward angles greater than 90°.

15. Electrons can’t back-scatter  particles. Calculate the maximum scattering angle— corresponding to the maximum momentum change. It can be shown that the maximum momentum transfer to the  particle is: Determine  max by letting  p max be perpendicular to the direction of motion: BeforeAfter too small!