Chem120A+Notes+-+Tunneling

Chem120A+Notes+-+Tunneling - Physical Chemistry Quantum...

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Physical Chemistry
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Quantum Mechanics Two striking predictions from quantum mechanics Theory Wave-particle duality Quantum tunneling
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Wave-Particle Duality Wave Character de Broglie relation λ= h / p λ the wave length, h Planck’s constant, p the momentum of particle For photon, p = E / c; For a particle with mass m , p = (2 mE ) 1/2 . Interference | ψ | 2 = | ψ 1 | 2 + | ψ 2 | 2 + | ψ 1 ψ 2 + ψ 1 ψ 2 | interference term Applications: Electron, Hellium Diffraction
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Wave-Particle Duality Particle Character Quantized energy of photon Ε = h ν h Planck’s constant ν the frequency of electromagnetic field Discrete energy levels of atoms and molecules Electronic energy levels Vibrational and rotational energy levels of molecules Electron and nuclear spin levels Application: Laser, XPS, Infrared spectroscopy, Raman spectroscopy, Sum Frequency Generation, Nuclear Magnetic Resonance, …
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Quantum Tunneling Even if the kinetic energy E is less than the barrier height V , there is a tunneling probability P = 16 ε (1- ε ) exp(-2 L / D ) where ε = Ε / V , D = ħ / [2 m ( V - E )] 1/2 , and m is the mass of the particle . . Ε V L Wavefunction Potential Energy Barrier Tunneling probability increases with the decrease of the barrier width L and the increase of D.
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Quantum Isotope Effect Estimate the relative probability that a proton and a deuteron can tunnel through the barrier of height 1.0 eV and length 100 pm when their energy is 0.9 eV. ( m D = 2 m H = 2 × 1.673 × 10 -27 , 1 eV = 1.602×10 -19 J ). 34 D -19 1/ 2 D 34 H -19 1/ 2 H 200(1/14 1/10) 2 H D H D 1.055 10 Js 10 pm [2 0.1 eV 1.602 10 ] 1.055 10 Js 14 pm [2 0.1 eV 1.602 10 ] 1 1 exp 2 e 3.0 10 D m D m P L P D D - - - - × = = × × × × × = = × × × × = - - = = × Lighter particles, such as electron and hydrogen atom, have stronger tunneling.
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