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Physical Chemistry 2 nd Edition Thomas Engel, Philip Reid Chapter 12 From Classic to Quantum Mechanics.

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Presentation on theme: "Physical Chemistry 2 nd Edition Thomas Engel, Philip Reid Chapter 12 From Classic to Quantum Mechanics."— Presentation transcript:

1 Physical Chemistry 2 nd Edition Thomas Engel, Philip Reid Chapter 12 From Classic to Quantum Mechanics

2 © 2010 Pearson Education South Asia Pte Ltd Physical Chemistry 2 nd Edition Chapter 12: From Classic to Quantum Mechanics Objectives Introduction of Quantum Mechanics Understand the difference of classical theory and experimental observations of quantum mechanics

3 © 2010 Pearson Education South Asia Pte Ltd Physical Chemistry 2 nd Edition Chapter 12: From Classic to Quantum Mechanics 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

4 © 2010 Pearson Education South Asia Pte Ltd Physical Chemistry 2 nd Edition Chapter 12: From Classic to Quantum Mechanics 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.

5 © 2010 Pearson Education South Asia Pte Ltd Physical Chemistry 2 nd Edition Chapter 12: From Classic to Quantum Mechanics 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.

6 © 2010 Pearson Education South Asia Pte Ltd Physical Chemistry 2 nd Edition Chapter 12: From Classic to Quantum Mechanics 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.

7 © 2010 Pearson Education South Asia Pte Ltd Physical Chemistry 2 nd Edition Chapter 12: From Classic to Quantum Mechanics 12.3 Blackbody Radiation Under the condition of equilibrium between the radiation field inside the cavity and the glowing piece of matter, where v = frequency ρ = spectral density T = temperature c = speed of light = average energy of an oscillating dipole in the solid

8 © 2010 Pearson Education South Asia Pte Ltd Physical Chemistry 2 nd Edition Chapter 12: From Classic to Quantum Mechanics 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.

9 © 2010 Pearson Education South Asia Pte Ltd Physical Chemistry 2 nd Edition Chapter 12: From Classic to Quantum Mechanics 12.3 Blackbody Radiation Blackbody RadiationBlackbody Radiation Max Planck derived the agreement between theory and experiment on radiation energy. 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.

10 © 2010 Pearson Education South Asia Pte Ltd Physical Chemistry 2 nd Edition Chapter 12: From Classic to Quantum Mechanics 12.3 Blackbody Radiation Introducing some classical physics, Max Planck obtained the following relationship:Max Planck A more general formula for the spectral radiation density from a blackbody is obtained.

11 © 2010 Pearson Education South Asia Pte Ltd Physical Chemistry 2 nd Edition Chapter 12: From Classic to Quantum Mechanics 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. photoelectric effect

12 © 2010 Pearson Education South Asia Pte Ltd Physical Chemistry 2 nd Edition Chapter 12: From Classic to Quantum Mechanics 12.4 The Photoelectric Effect Albert Einstein states that the energy of light,Albert Einstein where β = constant v = frequency From energy conservation the energy of the electron, E e, is where Ф = work function

13 © 2010 Pearson Education South Asia Pte Ltd Physical Chemistry 2 nd Edition Chapter 12: From Classic to Quantum Mechanics 12.4 The Photoelectric Effect The results of β is identical to Planck ’ s constant, h, thus

14 © 2010 Pearson Education South Asia Pte Ltd Physical Chemistry 2 nd Edition Chapter 12: From Classic to Quantum Mechanics 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.

15 © 2010 Pearson Education South Asia Pte Ltd Physical Chemistry 2 nd Edition Chapter 12: From Classic to Quantum Mechanics Solution We write and convert the units of from electron-volts to joules: Electrons will only be ejected if the photon energy, hv, is greater than. The photon energy is calculated to be which is sufficient to eject electrons.

16 © 2010 Pearson Education South Asia Pte Ltd Physical Chemistry 2 nd Edition Chapter 12: From Classic to Quantum Mechanics Solution We can obtain. Using, we calculate that

17 © 2010 Pearson Education South Asia Pte Ltd Physical Chemistry 2 nd Edition Chapter 12: From Classic to Quantum Mechanics 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 thatde Broglie where p = mv (particle momentum) Louis-Victor-Pierre-Raymond, 7th duc de Broglie

18 © 2010 Pearson Education South Asia Pte Ltd Physical Chemistry 2 nd Edition Chapter 12: From Classic to Quantum Mechanics 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=p 2 /2m for the kinetic energy, we obtain

19 © 2010 Pearson Education South Asia Pte Ltd Physical Chemistry 2 nd Edition Chapter 12: From Classic to Quantum Mechanics 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.

20 © 2010 Pearson Education South Asia Pte Ltd Physical Chemistry 2 nd Edition Chapter 12: From Classic to Quantum Mechanics 12.6 Diffraction by a Double Slit For diffraction of light from a thin slit, b >> a.

21 © 2010 Pearson Education South Asia Pte Ltd Physical Chemistry 2 nd Edition Chapter 12: From Classic to Quantum Mechanics 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.

22 © 2010 Pearson Education South Asia Pte Ltd Physical Chemistry 2 nd Edition Chapter 12: From Classic to Quantum Mechanics 12.6 Diffraction by a Double Slit The condition that the minima satisfy is where λ = wavelength 12.4 Diffraction from Double Slit

23 © 2010 Pearson Education South Asia Pte Ltd Physical Chemistry 2 nd Edition Chapter 12: From Classic to Quantum Mechanics 12.6 Diffraction by a Double Slit For double-slit diffraction experiment, Light and electron diffraction:

24 © 2010 Pearson Education South Asia Pte Ltd Physical Chemistry 2 nd Edition Chapter 12: From Classic to Quantum Mechanics Particle wave is from self-interference, NOT of the interference between particles 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.

25 © 2010 Pearson Education South Asia Pte Ltd Physical Chemistry 2 nd Edition Chapter 12: From Classic to Quantum Mechanics 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, of all lines in an atomic hydrogen spectrum is given by

26 © 2010 Pearson Education South Asia Pte Ltd Physical Chemistry 2 nd Edition Chapter 12: From Classic to Quantum Mechanics Example 12.3 Calculate the radius of the electron in H in its lowest energy state, corresponding to n =1. Solution: We have

27 © 2010 Pearson Education South Asia Pte Ltd Physical Chemistry 2 nd Edition Chapter 12: From Classic to Quantum Mechanics Random phase, coherent wave and laser Laser atom, molecule, cluster,….human? 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.

28 © 2010 Pearson Education South Asia Pte Ltd Physical Chemistry 2 nd Edition Chapter 12: From Classic to Quantum Mechanics A VERY BRIEF GLIMPSE OVER QUANTUM CHEMISTRY A VERY BRIEF GLIMPSE OVER QUANTUM CHEMISTRY Walter Heitler, Fritz London (VB)Walter HeitlerFritz London Wolfgang Pauli, John C. Slater, Linus Pauling (VB)Wolfgang PauliJohn C. SlaterLinus Pauling Friedrich Hund and Robert S. Mulliken, Erich Hückel ( MO )Friedrich HundRobert S. Mulliken Erich Hückel Douglas Hartree, Vladimir A. Fock, Clemens Roothaan (MO)Douglas HartreeVladimir A. FockClemens Roothaan Gerhard Herzberg (Molecular Spectroscopy)Gerhard Herzberg Roald Hoffman, Kenichi Fukui (Semi/Empirical)Roald HoffmanKenichi Fukui Rudolph A. Marcus, Henry Eyring (Transition State Theory)Rudolph A. MarcusHenry Eyring Dudley R. Herschbruk,Yuan-Tseh Lee, John Charles Polanyi, Ahmed Zewail (Reaction Dynamics)Dudley R. Herschbruk Yuan-Tseh LeeJohn Charles PolanyiAhmed Zewail John H. Van Vleck, John Pople, Walter Kohn, Robert G. Parr, Martin Karplus (Electrons in Solid, Density Functional Theory, Molecular Dyanmics)John H. Van Vleck John PopleWalter Kohn Robert G. ParrMartin Karplus

29 © 2010 Pearson Education South Asia Pte Ltd Physical Chemistry 2 nd Edition Chapter 12: From Classic to Quantum Mechanics Recommended Websites for Learning QChem Tutorial Materials: MIT OPEN COURSE: Forum: U tube: U tube: search ‘quantum chemistry’ or ‘quantum mechanics’. Chemical Bond: Computation/simulation software: Nobel laureates 中文網站可自行搜索關鍵詞:量子化學


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