量子力学和原子理论

1、Larry Shen,Quantum Mechanics and Atomic Theory,Classical Physics,Classical mechanics Maxwells theory of electricity, magnetism and electro-magnetic radiation Thermodynamics Kinetic theory,Eletromagnetic Radiation,Class radiation,Blackbody Radiation,Ultraviolet Catastrophe(紫外線崩潰),The classical theory

2、 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.,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

3、發散的，與實驗明顯不符，即 ultraviolet catastrophe,長波長 短波長,By combining the formulae of Wien and Rayleigh, Planck announced in October 1900 a formula now known as Plancks radiation formula.,Max Planck,18581947 Planck initiated the study of quantum mechanics when he announced in 1900 his theoretical research into

4、 the radiation and absorption of heat/light by a black body.,Max Plancks Theory,The Nobel Prize in Physics 1918,h: Plancks constant k: Boltzmanns constant C: speed of light v: frequency of light,Plancks Impacts,In classical physics, energy is a continuous variable. Planck defined the amount of energ

5、y, a quantum of energy, E=nhn In quantum physics, the energy of a system is quantized.,Albert Einstein,18791955 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 mode

6、l of the large-scale universe that we have.,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 metals surface,The wave nature of electrons,Louis de Broglie, The Nobel Prize in Physi

7、cs 1929 光具有物質與波雙重性質 =h/mv,Light waves,Werner Heisenberg,19011976 Werner Heisenberg did important work in Quantum Mechanics as well as nuclear physics.,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,The Atomic Spectrum of Hydrogen,The Bohr Model

8、,Niel Bohr The Nobel Prize in Physics 1922,The electron in a hydrogen atom moves around the nucleus only in certain allowed circular orbits.,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,Quantum Mechanics,By the mid-1920s, Werner Karl Hei

9、senberg, Louis de Broglie and Erwin Schrdinger developed the wave mechanics or more commonly, quantum mechanics.,Tunnel Effect,Quantum effect in biological systems,Rudolph A. Marcus was awarded the 1992 Nobel Prize in Chemistry. Marcus theory Electron transfer reactions,Schrdinger Equation,Particle

10、in a box,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.,Three energy levels,Three Dimension Box,Degenercy,E,Lx=Ly=Lz,The spherical polar

11、coordinate system,The Wave Function for the Hydrogen Atom,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. 2:probability distribution dv: small volume element,The probability

12、distribution for the hydrogen 1s orbital Calculate the probability at points along a line drawn outward in any direction from nucleus.,number of nodes=n-1,nodes,The radial probability distribution for the hydrogen 1s orbital in spherical shell Bohr radius: 0.529 Denoted by a0,0.529,Relative Orbital

13、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=1.4,Quantum Numbers,n: the principal quantum number l: the angular momentum quantum number Ml: the magnetic q

14、uantum number,Quantum Numbers principal 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,Quantum Numbers ang

15、ular momentum quantum number (l),Have integral values from 0 to n-1. Determines the shapes of the atomic orbital.,Quantum Numbers magnetic 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.,2P

16、x,n value,l Value,Orientation in space,Electron Spin and Pauli Principle,electron spin quantum number (ms): +1/2 and -1/2 Pauli Principle: In a given atom, no two electrons can have the same set of four quantum numbers (n, l, ml, ms),Polyelectronic Atoms,the kinetic energy of the electrons as they m

17、ove around the nucleus the potential energy of attraction between the nucleus and the electrons the potential energy of repulsion between the two electrons First ionization energy: 2372 kJ/mol Second ionization energy: 5248 kJ/mol,Hydrogen Like Approximation,Zeff=Zactual-(effect of electron repulsio

18、ns) 1Zeff2 Substituting Zeff in place of Z=1 in the hydrogen wave mechanical equations,2+,e-,e-,Zeff+,e-,Actual He atom,Hypothetical He atom,Valence electrons and Core electrons,Valence electrons: the electrons in the outermost principal quantum level of an atom. Core electrons: inner electrons,Pene

19、tration effect,Core electrons,Na:1s22s22p63s1,K: 1s22s22p63s23p64s1,Aufbau principle,The physical and chemical properties of elements is determined by the atomic structure. The atomic structure is, in turn, determined by the electrons and which shells, subshells and orbitals they reside in. The rule

20、s of placing electrons within shells is known as the Aufbau principle. As protons are added one by one to the nucleus to build up the elements, electrons are similarly added to these atomic orbitals.,Ionization Energy,X(g) X+(g)+e- The ionization energy for a particular electron in an atom is a source of information about the energy of the orbital it occupies in the atom. Resulting ion will not reorganize