The Nuclear Atom

1. The Nuclear Atom Wei-Li Chen 10/23/2012

2. Dispersion red blue

4. J. J. Thomson’s Model Electrons are embedded in positively charged liquid. If atoms

5. Rutherford’s Nuclear Model • Thomson’s atomic model can not explain the Rydberg-Ritz formula. • In Geiger and Marsden’s experiment, most α particles are deflected by very small angles less than 1 degree. • Some particles are deflected by large angles near 180 degree, which can not be explained by Thomson’s atomic model. • In Rutherford’s atomic model, all the positive charges and most of the mass are confined in a very small “nucleus” of the atom.

6. Rutherford’s Nuclear Model scattering angle Impact parameter

8. Geiger and Marsden’s Experiment

10. Assuming nuclei do not overlap on the beam path. It is justified by the extreme small size of the nucleus. atom

11. Zis different

12. The Size of the Nucleus Deviation from prediction

13. Electron Orbits • Based on Rutherford’s experimental results, the mass of the atom concentrating in a tiny volume at the center of the atom. • Electrons must circulate the nucleus on an circular or elliptical orbits to maintain a stable system. • However, a negatively charged electron moving on an circular orbit must radiate electromagnetic waves according to classical physics. The radius of the orbit will decrease and the electron will finally reach the nucleus. This prediction is contrary to the experimental observation.

15. Bohr’s Theory • When an electron is in one of the quantized orbits, it does not emit any electromagnetic radiation; thus, the electron is said to be in a stationary state. • The electron can make a discontinuous emission, or quantum jump, from one stationary state to another. During this transition it does emit radiation. When an electron makes a transition from one stationary state to another, the energy difference ∆E is released as a single photon of frequency ν= ∆E /h ( or h ν= Ei-Ef ). • In the limit of large orbits and large energies, quantum calculations must agree with classical calculations. (correspondence principle) • The permitted orbits are characterized as quantized values of the orbital angular momentum. This angular momentum is always an integer multiple of h/2π.

18. Spectrum of Atomic Hydrogen

19. Reduced Mass Correction

20. Correspondence Principle

21. Wilson-Sommerfeld Quantization Rule

22. Px x 1D Simple Harmonic Oscillator

23. Circular Orbit (Bohr’s H Atom) Standing wave can be used to explain The stationary state concept in Bohr’s model.

24. energy splitting Fine Structures of H atom

25. X-ray Spectra

26. Mosley Plot

28. n=3 n=2 KLM Auger process n=1 Auger Electrons Different atoms have different spectrum

29. Auger Electron Spectroscopy Differentiated data

30. Accelerating voltage I Hg gas V0 Franck-Hertz Experiment ∆V≠0, with gas, the current drops periodically ∆V=0, no gas, the maximum current Is limited by the filament

31. ∆E=E2-E1

32. If the electron energy is absorbed by an atom to induce electron transition, the amount of the energy transferred will be quantized. From grid to plate, this process could happen multiple times, therefore a periodical reduction in current is observed.

33. Electron Energy Loss Spectroscopy (EELS) The energy structures of various atoms are different. The energy loss spectrum of the incident electrons is also different. EELS can be used to identify atoms and explore the quantized energy structures.

34. Critique of Bohr Theory • In Bohr’s model, the H atom spectra and X-rays were successfully explained. However, the quantitative analysis was absent. The transition rate that a particular transition (ie. the intensity of the lines) can not be predicted by Bohr’s model. This lead us to the development of thequantum mechanicsorwave mechanics.