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Chapter 12 From Classic to Quantum Mechanics Physical Chemistry 2nd Edition Thomas Engel, Philip Reid Objectives • Introduction of Quantum Mechanics • Understand the difference of classical theory and experimental observations of quantum mechanics Chapter 12: From Classic to Quantum Mechanics Physical Chemistry 2nd Edition © 2010 Pearson Education South Asia Pte Ltd Outline 1. Why Study Quantum Mechanics? 2. Quantum Mechanics Arose Out of the Interplay of Experiments and Theory 3. Blackbody Radiation 4. The Photoelectric Effect 5. Particles Exhibit Wave-Like Behavior 6. Diffraction by a Double Slit 7. Atomic Spectra and the Bohr Model of the Hydrogen Atom Chapter 12: From Classic to Quantum Mechanics Physical Chemistry 2nd Edition © 2010 Pearson Education South Asia Pte Ltd 12.1 Why Study Quantum Mechanics? • Quantum mechanics predicts that atoms and molecules can only have discrete energies. • Quantum mechanical calculations of chemical properties of molecules are reasonably accurate. Chapter 12: From Classic to Quantum Mechanics Physical Chemistry 2nd Edition © 2010 Pearson Education South Asia Pte Ltd 12.2 Quantum Mechanics Arose Out of the Interplay of Experiments and Theory • Two key properties are used to distinguish classical and quantum physics. 1. Quantization - Energy at the atomic level is not a continuous variable, but in discrete packets called quanta. 2. Wave-particle duality - At the atomic level, light waves have particle-like properties, while atoms and subatomic particles have wave-like properties. Chapter 12: From Classic to Quantum Mechanics Physical Chemistry 2nd Edition © 2010 Pearson Education South Asia Pte Ltd 12.3 Blackbody Radiation • • An ideal blackbody is a cubical solid at a high temperature emits photons from an interior spherical surface. The reflected photons ensure that the radiation is in thermal equilibrium with the solid. Chapter 12: From Classic to Quantum Mechanics Physical Chemistry 2nd Edition © 2010 Pearson Education South Asia Pte Ltd 12.3 Blackbody Radiation • Under the condition of equilibrium between the radiation field inside the cavity and the glowing piece of matter, 8v 2 pv, T dv 3 EOSC dv c where v = frequency ρ = spectral density T = temperature c = speed of light EOSC = average energy of an oscillating dipole in the solid Chapter 12: From Classic to Quantum Mechanics Physical Chemistry 2nd Edition © 2010 Pearson Education South Asia Pte Ltd 12.3 Blackbody Radiation • 12.1 and 12.2 Blackbody Radiation • Spectral density is the energy stored in the electromagnetic field of the blackbody radiator. Chapter 12: From Classic to Quantum Mechanics Physical Chemistry 2nd Edition © 2010 Pearson Education South Asia Pte Ltd 12.3 Blackbody Radiation • Max Planck derived the agreement between theory and experiment on radiation energy. E nhv where h = Planck’s constant n = a positive integer (n 0, 1, 2, . . . ) • The theory states that the energies radiated by a blackbody are not continuous, but can take discrete values for each frequency. Chapter 12: From Classic to Quantum Mechanics Physical Chemistry 2nd Edition © 2010 Pearson Education South Asia Pte Ltd 12.3 Blackbody Radiation • Introducing some classical physics, Max Planck obtained the following relationship: EOSC • hv e hv / kT 1 A more general formula for the spectral radiation density from a blackbody is obtained. 8hv 3 1 pv, T 3 dv hv / kT c e 1 Chapter 12: From Classic to Quantum Mechanics Physical Chemistry 2nd Edition © 2010 Pearson Education South Asia Pte Ltd 12.4 The Photoelectric Effect • • The electrons emitted by the surface upon illumination are incident on the collector, which is at an appropriate electrical potential to attract them. This is called the photoelectric effect. Chapter 12: From Classic to Quantum Mechanics Physical Chemistry 2nd Edition © 2010 Pearson Education South Asia Pte Ltd 12.4 The Photoelectric Effect • Albert Einstein states that the energy of light, E v • where β = constant v = frequency From energy conservation the energy of the electron, Ee, is Ee v where Ф = work function Chapter 12: From Classic to Quantum Mechanics Physical Chemistry 2nd Edition © 2010 Pearson Education South Asia Pte Ltd 12.4 The Photoelectric Effect • The results of β is identical to Planck’s constant, h, thus E hv Chapter 12: From Classic to Quantum Mechanics Physical Chemistry 2nd Edition © 2010 Pearson Education South Asia Pte Ltd Example 12.1 Light with a wavelength of 300 nm is incident on a potassium surface for which the work function, , is 2.26 eV. Calculate the kinetic energy and speed of the ejected electrons. Chapter 12: From Classic to Quantum Mechanics Physical Chemistry 2nd Edition © 2010 Pearson Education South Asia Pte Ltd Solution We write Ee hv hc / and convert the units of from electron-volts to joules: 2.26eV 1.602 1019 J / eV 3.62 1019 J Electrons will only be ejected if the photon energy, hv, is greater than . The photon energy is calculated to be hc 6.626 10 2.998 10 6.62 10 34 300 10 8 9 which is sufficient to eject electrons. Chapter 12: From Classic to Quantum Mechanics Physical Chemistry 2nd Edition © 2010 Pearson Education South Asia Pte Ltd 19 J Solution We can obtain Using Ee hc / 2.99 10 19 J Ee 1 / 2mv2 . , we calculate that 2 Ee 22.99 1019 J 5 v 8 . 10 10 m/ s 31 m 9.109 10 Chapter 12: From Classic to Quantum Mechanics Physical Chemistry 2nd Edition © 2010 Pearson Education South Asia Pte Ltd 12.5 Particles Exhibit Wave-Like Behavior • • Louis de Broglie suggested a relationship between momentum and wavelength for light applying to particles. The de Broglie relation states that h p where p = mv (particle momentum) Louis-Victor-Pierre-Raymond, 7th duc de Broglie Chapter 12: From Classic to Quantum Mechanics Physical Chemistry 2nd Edition © 2010 Pearson Education South Asia Pte Ltd Example 12.2 Electrons are used to determine the structure of crystal surfaces. To have diffraction, the wavelength of the electrons should be on the order of the lattice constant, which is typically 0.30 nm. What energy do such electrons have, expressed in electron-volts and joules? Solution: Using E=p2/2m for the kinetic energy, we obtain E 34 2 p h 6.626 10 18 2 . 7 10 or 17eV 2 31 10 2m 2m 2 9.109 10 3.0 10 2 2 Chapter 12: From Classic to Quantum Mechanics Physical Chemistry 2nd Edition © 2010 Pearson Education South Asia Pte Ltd 12.6 Diffraction by a Double Slit • 12.3 Diffraction of Light • Diffraction is a phenomenon that can occur with any waves, including sound waves, water waves, and electromagnetic (light) waves. Chapter 12: From Classic to Quantum Mechanics Physical Chemistry 2nd Edition © 2010 Pearson Education South Asia Pte Ltd 12.6 Diffraction by a Double Slit • For diffraction of light from a thin slit, b >> a. Chapter 12: From Classic to Quantum Mechanics Physical Chemistry 2nd Edition © 2010 Pearson Education South Asia Pte Ltd 12.6 Diffraction by a Double Slit • Maxima and minima arise as a result of a path difference between the sources of the cylindrical waves and the screen. Chapter 12: From Classic to Quantum Mechanics Physical Chemistry 2nd Edition © 2010 Pearson Education South Asia Pte Ltd 12.6 Diffraction by a Double Slit • The condition that the minima satisfy is n sin , n 1,2,3,..... a where λ = wavelength • 12.4 Diffraction from Double Slit Chapter 12: From Classic to Quantum Mechanics Physical Chemistry 2nd Edition © 2010 Pearson Education South Asia Pte Ltd 12.6 Diffraction by a Double Slit • For double-slit diffraction experiment, Light and electron diffraction: http://physics-animations.com/Physics/English/top_ref.htm#elin Chapter 12: From Classic to Quantum Mechanics Physical Chemistry 2nd Edition © 2010 Pearson Education South Asia Pte Ltd Particle wave is from self-interference, NOT of the interference between particles Which slit does an electron pass through? We do not know—if we observe the interference. One of the slits each time (via observation)—if we do not observed interference. Chapter 12: From Classic to Quantum Mechanics Physical Chemistry 2nd Edition © 2010 Pearson Education South Asia Pte Ltd 12.7 Atomic Spectra and the Bohr Model of the Hydrogen of the Hydrogen Atom • Light is only observed at certain discrete wavelengths, which is quantized. For the emission spectra, the inverse of the wavelength, 1/ v~ of all lines in an atomic hydrogen spectrum is given by • 1 1 1 1 ~ v cm RH cm 2 2 , n n1 n1 n Chapter 12: From Classic to Quantum Mechanics Physical Chemistry 2nd Edition © 2010 Pearson Education South Asia Pte Ltd Example 12.3 Calculate the radius of the electron in H in its lowest energy state, corresponding to n =1. Solution: We have 40 h 2 n 2 4 8.85419 10 12 1.0555 10 34 12 r 2 31 19 2 me e 9.109 10 1.6022 10 5.292 10 11 m Chapter 12: From Classic to Quantum Mechanics Physical Chemistry 2nd Edition © 2010 Pearson Education South Asia Pte Ltd Random phase, coherent wave and laser Ae A1e i (1t 1 ) A2e i (t ) i (2t 2 ) A3e i (3t 3 ) ... When all phases are fixed or have fixed relationship, these waves are called coherent. Otherwise, when the phases are different and have no correlations, these waves are in random phases. Chapter 12: From Classic to Quantum Mechanics Physical Chemistry 2nd Edition © 2010 Pearson Education South Asia Pte Ltd Laser atom, molecule, cluster,….human? A VERY BRIEF GLIMPSE OVER QUANTUM CHEMISTRY • • • • • • • • Walter Heitler, Fritz London (VB) Wolfgang Pauli, John C. Slater, Linus Pauling (VB) Friedrich Hund and Robert S. Mulliken, Erich Hückel (MO) Douglas Hartree , Vladimir A. Fock, Clemens Roothaan (MO) Gerhard Herzberg (Molecular Spectroscopy) Roald Hoffman, Kenichi Fukui (Semi/Empirical) Rudolph A. Marcus, Henry Eyring (Transition State Theory) Dudley R. Herschbruk ,Yuan-Tseh Lee, John Charles Polanyi, Ahmed Zewail (Reaction Dynamics) • John H. Van Vleck, John Pople, Walter Kohn, Robert G. Parr, Martin Karplus (Electrons in Solid, Density Functional Theory, Molecular Dyanmics) Chapter 12: From Classic to Quantum Mechanics Physical Chemistry 2nd Edition © 2010 Pearson Education South Asia Pte Ltd Recommended Websites for Learning QChem Tutorial Materials: • MIT OPEN COURSE: http://ocw.mit.edu/OcwWeb/Chemistry/ Forum: • http://iopenshell.usc.edu/forum/topic.php?id=52 U tube: search ‘quantum chemistry’ or ‘quantum mechanics’. Chemical Bond: • http://osulibrary.oregonstate.edu/specialcollections/coll/pauling/bond/index.html Computation/simulation software: • http://en.wikipedia.org/wiki/Quantum_chemistry_computer_programs • http://en.wikipedia.org/wiki/Molecular_modelling Nobel laureates • http://en.wikipedia.org/wiki/Category:Nobel_laureates_in_Chemistry Chapter 12: From Classic to Quantum Mechanics Physical Chemistry 2nd Edition © 2010•Pearson Education South Asia Pte Ltd 中文網站可自行搜索關鍵詞:量子化學