Chapter 30

1. Chapter 30 The Nature of the Atom

2. Rutherford Scattering and the Nuclear Atom Line Spectra The Bohr Model of the Hydrogen Atom The De Broglie Explanation of Bohr’s Assumption about Angular Momentum The Quantum Mechanical Picture of the Hydrogen Atom The Pauli Exclusion Principle and the Periodic Table of the Elements X-Rays The Laser Medical Applications of the Laser Holography Outline

3. 1- Rutherford scattering and the nuclear atom Thomson’s early model Geiger & Marsden experiment Rutherford model

4. In its natural state, an atom is electrically neutral.

5. 2- Line Spectra

6. ExamplesofSpectra Emission in the visible range HYDROGEN Absorption in the visible range

7. Emission Spectrum of Hydrogen: The Balmer Series • The wavelengths of hydrogen’s spectral lines can be found from • RH is the Rydberg constant • RH = 1.0973732 x 107 m-1 • n is an integer, n> 2, 3, … • The spectral lines correspond to different values of n

8. Spectral LinesofHydrogen Examples of spectral lines • n = 3, l= 656.3 nm • n = 4, l = 486.1 nm

9. All the Spectral LinesofHydrogen Lyman series Balmer series Paschen series

10. 3- The Bohr model of the Hydrogen atom Assumptions: • e- follows a circular orbit about the proton • Orbits are stable and discrete • Radiation: the electron jumps from one orbital to another : Ei – Ef = hn • Electron orbital momentum: me v r = n ħ where n = 1, 2, 3, … ħ = h / 2p

11. The total energy of the atom

12. So that the orbits are discrete 0.0529nm (Bohr radius) Allowed energies for the Hydrogen atom Ground state: n = 1

13. n = 3 hn n = 2 n = 1 Electronic transitions

14. 11 Transitions occur from ni to nf (ni > nf ) Example Balmer series : nf = 2 (visible emission) Bohr’s theory predicted all observed spectral lines of Hydrogen. n = 3 hn n = 2 1 n = 1

15. ( nf = 3 ) ( nf = 2 ) ( nf = 1)

16. ExamplesofSpectra Emission in the visible range HYDROGEN Absorption in the visible range

17. Bohr’s Correspondence Principle • n is very large  energy levels are continuous  classical treatment ( Emission frequency = frequency of revolution of the electron) • Bohr’s Correspondence Principle states that quantum mechanics is in agreement with classical physics when the energy differences between quantized levels are very small

18. Modification of the Bohr Theory • Bohr’s model applies to Hydrogen – Like atoms ( containing 1electron ) such as He+, Li+ +, Be3+… • It leads to the modification of the emitted ls

19. 4- De Broglie’s explanation of Bohr’s assumption about angular momentum l Standing wave pattern LAB = n.l

20. n, principal quantum number = Energy of the states ( shells : K, L, M…) ℓ, orbital quantum number, can vary from 0 to n - 1 in integer steps ( sub – shells: max nb of electrons: 2 (2 ℓ + 1) ) n = 1 (K)  ℓ = 0 1s subshell (2 e-) n = 2 (L)  ℓ = 0 2s (2 e-) ℓ = 1 2p (6 e-) n = 3 (M)  ℓ = 0 3s (2 e-) ℓ = 1 3p (6 e-) ℓ = 2 3d (10 e-) 5- The quantum mechanical picture of the hydrogen atom

21. 3. m ℓ = orbital magnetic quantum number can vary from - ℓ to + ℓ in integer steps. Important when a magnetic field is applied! (2 ℓ + 1) values 4. ms = spin magnetic quantum number; ms = + 1/2 or – 1/2 . Electron spinning about its axis

23. Example 5 The Bohr Model Versus Quantum Mechanics Determine the number of possible states for the hydrogen atom when the principal quantum number is (a) n=1 and (b) n=2.

25. Physical significance of the quantum numbers n • n = 1  K shell • n = 2  L shell • n = 3  M shell • n = 4  N shell

26. ℓ Quantization of the orbit momentum • K  n = 1  ℓ = 0 • L  n = 2  ℓ = 0  L = 0 (s) ℓ = 1 

27. m ℓ • Projection of L along the z - axis

28. electron spinning on its own axis. There are two directions for the spin Spin up, ms = ½ Spin down, ms = -½ ms

29. The Electron Cloud Probability of finding an electron versus distance

32. 6- The Pauli exclusion principle and the periodic table of the elements Generally, the energy increases with increasing n. There are exceptions to the general rule.

33. Consider an electronic state defined by: n, ℓ, mℓ, and ms • No two electrons in an atom can ever be in the same quantum state • In other words, no two electrons in the same atom can have exactly the same values for n, ℓ, mℓ, and ms • Electronic Configuration of the elements Mendeleev Table

34. 1s2 2s2 3s2 2p6 3p6 3d10 Allowed Quantum numbers for an Atom up to n = 3

38. 7- X-Rays • When a metal target is bombarded by high-energy electrons, x-rays are emitted Bremsstrahlung

39. Mechanism • X- ray emission: electron drops from a higher to a lower energy level (filling the vacancy) • The energy of the emitted photon is equal to the difference between the energy of the two corresponding levels

40. Energy levels determination • Two electrons in the K-shell of an atom whose atomic number is Z • Partial screening • Zeff = ( Z - 1)e

41. Modified form of the energy of each electron: L-shells electrons  M-shells electrons 

42. 8- The Laser Light Amplification by Stimulated Emission of Radiation Stimulated absorption: DE = hƒ = E2 – E1

43. Spontaneous emission

44. Stimulated emission:

45. Population inversion • Situation whereby the system of atoms has a higher number of atoms in their excited state than in the ground state.

46. The “Lasing” process: • Monochromatic • Monophase • Highly directional

47. Population inversion • E3 , metastable state (relatively long life-time) • Stimulated emission of radiation UV, IR, VIS (He – Ne, Ar, CO2, Dye, Nd – YAG …

50. 9- Medical applications of the laser Lasers being used to change the shape of the cornea.