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

2. Objectives Introduction of Quantum Mechanics
Understand the difference of classical theory and experimental observations of quantum mechanics

3. 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

4. 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. 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.

6. 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. 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. 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. 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.

10. 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.

11. 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.

12. 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

13. 12.4 The Photoelectric Effect
The results of β is identical to Planck’s constant, h, thus

14. 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. 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. Solution
We can obtain
Using , we calculate that

17. 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

18. 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

19. 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. 12.6 Diffraction by a Double Slit
For diffraction of light from a thin slit, b >> a.

21. 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. 12.6 Diffraction by a Double Slit
The condition that the minima satisfy is
where λ = wavelength
12.4 Diffraction from Double Slit

23. 12.6 Diffraction by a Double Slit
For double-slit diffraction experiment,
Light and electron diffraction:

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

27. 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?

28. 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)

29. 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