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Chapter 12

Chapter 12. Quantum Mechanics and Atomic Theory. Classical Physics. Classical mechanics Maxwell’s theory of electricity, magnetism and electro-magnetic radiation Thermodynamics Kinetic theory. Eletromagnetic Radiation. Class radiation. Blackbody Radiation.

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Chapter 12

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  1. Chapter 12 Quantum Mechanics and Atomic Theory

  2. Classical Physics • Classical mechanics • Maxwell’s theory of electricity, magnetism and electro-magnetic radiation • Thermodynamics • Kinetic theory

  3. Eletromagnetic Radiation

  4. Class radiation

  5. Blackbody Radiation

  6. Ultraviolet Catastrophe(紫外線崩潰) The classical theory of matter, which assumes that matter can absorb or emit any quantity of energy, predicts a radiation profile that has no maximum and goes to infinite intensity at very short wavelengths.

  7. 古典理論解釋失敗 1900年，J.W.Rayleigh，J.H.Jeans根據 古典電動力學和統計物理理論，得出 一黑體輻射公式， 即Rayleigh-Jeans law。此公式只在低 頻部分與實驗曲線比較符合，高頻部 分是發散的，與實驗明顯不符，即 ultraviolet catastrophe

  8. By combining the formulae of Wien and Rayleigh, Planck announced in October 1900 a formula now known as Planck's radiation formula. 長波長 短波長

  9. 1858~1947 Planck initiated the study of quantum mechanics when he announced in 1900 his theoretical research into the radiation and absorption of heat/light by a black body. Max Planck

  10. Max Planck’s Theory The Nobel Prize in Physics 1918 h: Planck’s constant k: Boltzmann’s constant C: speed of light v: frequency of light

  11. Planck’s Impacts • In classical physics, energy is a continuous variable. • Planck defined the amount of energy, a quantum of energy, ∆E=nhn • In quantum physics, the energy of a system is quantized.

  12. 1879~1955 Einstein contributed more than any other scientist to the modern vision of physical reality. His special and general theories of relativity are still regarded as the most satisfactory model of the large-scale universe that we have. Albert Einstein

  13. Photoelectric Effect Albert Einstein, The Nobel Prize in Physics 1921 KEelectron=1/2mv2=hv-hv0 hv: energy of incident photon hv0: energy required to remove electron from metal’s surface

  14. The wave nature of electrons Louis de Broglie, The Nobel Prize in Physics 1929 光具有物質與波雙重性質 λ=h/mv

  15. Light waves

  16. 1901~1976 Werner Heisenberg did important work in Quantum Mechanics as well as nuclear physics. Werner Heisenberg

  17. Uncertainty Principle Werner Karl Heisenberg The Nobel Prize in Physics 1932 任何一個粒子無法將位置與動量同時 很精確的量測出來

  18. The Atomic Spectrum of Hydrogen

  19. The Bohr Model Niel Bohr The Nobel Prize in Physics 1922

  20. The electron in a hydrogen atom moves around the nucleus only in certain allowed circular orbits.

  21. 量子發展如同瞎子摸象 • Max Planck－能量不連續 • Albert Einstein－能階概念 • Louis de Broglie－粒子波動 • Werner Heisenberg－粒子運動測不準 • Niel Bohr－光波不連續

  22. Quantum Mechanics • By the mid-1920s, Werner Karl Heisenberg, Louis de Broglie and Erwin SchrÖdinger developed the wave mechanics or more commonly, quantum mechanics.

  23. Tunnel Effect

  24. Quantum effect in biological systems • Rudolph A. Marcus was awarded the 1992 Nobel Prize in Chemistry. • Marcus theory • Electron transfer reactions

  25. SchrÖdinger Equation

  26. Particle in a box

  27. Boundary Conditions • The particle cannot be outside the box-it is bound inside the box. • In a given state the total probability of finding the particle in the box must be 1. • The wave function must be continuous.

  28. Three energy levels

  29. Three Dimension Box

  30. Degenercy Lx=Ly=Lz E

  31. The spherical polar coordinate system

  32. The Wave Function for the Hydrogen Atom

  33. The Physical Meaning of a Wave Function • The square of the function evaluated at a particular point in space indicates the probability of finding an electron near that point. Ψ2:probability distribution dv: small volume element

  34. The probability distribution for the hydrogen 1s orbital Calculate the probability at points along a line drawn outward in any direction from nucleus.

  35. number of nodes=n-1 nodes

  36. The radial probability distribution for the hydrogen 1s orbital in spherical shell Bohr radius: 0.529Å Denoted by a0 0.529Å

  37. Relative Orbital Size • The normally accepted arbitrary definition of the size of the hydrogen 1s orbital is the radius of the sphere that encloses 90% of the total electron probability. • For H(1s), r(1s)=2.6a0=1.4Å

  38. Quantum Numbers • n: the principal quantum number • l: the angular momentum quantum number • Ml: the magnetic quantum number

  39. Quantum Numbersprincipal quantum number (n) • Have integral values (1,2,3…) • It is related to the size and energy of orbital. • As n increases, the orbital becomes larger and the electron spends more time farther from the nucleus • An increase in n also means higher energy

  40. Quantum Numbersangular momentum quantum number (l) • Have integral values from 0 to n-1. • Determines the shapes of the atomic orbital.

  41. Quantum Numbersmagnetic quantum number (ml) • Have integral values between l and –l, including zero. • Relates to the orientation in space of angular momentum associated with the orbital.

  42. n value 2Px Orientation in space l Value

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