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**Physical Chemistry 2nd Edition**

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

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**Objectives Introduction of Quantum Mechanics**

Understand the difference of classical theory and experimental observations of quantum mechanics

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**Outline Why Study Quantum Mechanics?**

Quantum Mechanics Arose Out of the Interplay of Experiments and Theory Blackbody Radiation The Photoelectric Effect Particles Exhibit Wave-Like Behavior Diffraction by a Double Slit Atomic Spectra and the Bohr Model of the Hydrogen Atom

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**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.

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**12.2 Quantum Mechanics Arose Out of the Interplay of Experiments and Theory**

Two key properties are used to distinguish classical and quantum physics. Quantization - Energy at the atomic level is not a continuous variable, but in discrete packets called quanta. Wave-particle duality - At the atomic level, light waves have particle-like properties, while atoms and subatomic particles have wave-like properties.

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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.

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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

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**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.

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12.3 Blackbody 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.

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12.3 Blackbody Radiation Introducing some classical physics, Max Planck obtained the following relationship: A more general formula for the spectral radiation density from a blackbody is obtained.

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**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.

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**12.4 The Photoelectric Effect**

Albert Einstein states that the energy of light, where β = constant v = frequency From energy conservation the energy of the electron, Ee, is where Ф = work function

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**12.4 The Photoelectric Effect**

The results of β is identical to Planck’s constant, h, thus

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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.

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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.

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Solution We can obtain Using , we calculate that

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**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 where p = mv (particle momentum) Louis-Victor-Pierre-Raymond, 7th duc de Broglie

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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

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**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.

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**12.6 Diffraction by a Double Slit**

For diffraction of light from a thin slit, b >> a.

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**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.

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**12.6 Diffraction by a Double Slit**

The condition that the minima satisfy is where λ = wavelength 12.4 Diffraction from Double Slit

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**12.6 Diffraction by a Double Slit**

For double-slit diffraction experiment, Light and electron diffraction:

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**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.

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**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

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Example 12.3 Calculate the radius of the electron in H in its lowest energy state, corresponding to n =1. Solution: We have

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**Random phase, coherent wave and laser**

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. Laser atom, molecule, cluster,….human?

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**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)

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**Recommended Websites for Learning QChem**

Tutorial Materials: MIT OPEN COURSE: Forum: 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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