physical chemistry 2 nd edition thomas engel, philip reid chapter 12 from classic to quantum...

Physical Chemistry 2Physical Chemistry 2ndnd Edition EditionThomas Engel, Philip Reid

Chapter 12 Chapter 12 From Classic to Quantum MechanicsFrom Classic to Quantum Mechanics

© 2010 Pearson Education South Asia Pte Ltd

Physical Chemistry 2nd EditionChapter 12: From Classic to Quantum Mechanics

ObjectivesObjectives

• Introduction of Quantum Mechanics• Understand the difference of classical

theory and experimental observations of quantum mechanics



OutlineOutline

1. Why Study Quantum Mechanics?2. Quantum Mechanics Arose Out of the

Interplay of Experiments and Theory3. Blackbody Radiation4. The Photoelectric Effect5. Particles Exhibit Wave-Like Behavior6. Diffraction by a Double Slit7. Atomic Spectra and the Bohr Model of the

Hydrogen Atom



12.1 Why Study 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.



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



12.3 Blackbody Radiation12.3 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.




• Under the condition of equilibrium between the radiation field inside the cavity and the glowing piece of matter,

where v = frequencyρ = spectral density

T = temperature c = speed of light

= average energy of an oscillating dipole in the solid

dvEc

vdvTvp OSC3

28,

OSCE




• 12.1 and 12.2 Blackbody Radiation

• Spectral density is the energy stored in the electromagnetic field of the blackbody radiator.



12.3 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.

nhvE




• Introducing some classical physics, Max Planck obtained the following relationship:

• A more general formula for the spectral radiation density from a blackbody is obtained.

1/

kThvOSC e

hvE

dvec

hvTvp

kThv 1

18,

/3

3



12.4 The Photoelectric Effect12.4 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.




• 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

vEe

vE




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

hvE



Example 12.1Example 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.



SolutionSolution

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.

/hchvEe

JeVJeV 1919 1062.3/10602.126.2

J

hc 199

834

1062.610300

10998.210626.6



SolutionSolution

We can obtain .

Using , we calculate that

sm

J

m

Ev e /1010.8

10109.9

1099.222 531

19

22/1 mvEe

JhcEe191099.2/



12.5 Particles Exhibit Wave-Like Behavior12.5 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)

p

h

Louis-Victor-Pierre-Raymond, 7th duc de Broglie




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

eVm

h

m

pE 17or 107.2

100.310109.92

10626.6

2218

1031

234

2

22



12.6 Diffraction by a Double Slit12.6 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.




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




• Maxima and minima arise as a result of a path difference between the sources of the cylindrical waves and the screen.




• The condition that the minima satisfy is

where λ = wavelength

• 12.4 Diffraction from Double Slit

.....,3,2,1,sin na

n




• For double-slit diffraction experiment,

Light and electron diffraction:http://physics-animations.com/Physics/English/top_ref.htm#elin



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.



12.7 Atomic Spectra and the Bohr Model of 12.7 Atomic Spectra and the Bohr Model of the the Hydrogen of the Hydrogen Atom 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

1221

11 ,11~ nnnn

cmRcmv H

v~/1




Calculate the radius of the electron in H in its lowest energy state, corresponding to n =1.

Solution:We have

m 10292.5

106022.110109.9

1100555.11085419.844

11

21931

23412

2

220

em

nhr

e



Random phase, coherent wave and Random phase, coherent wave and laser laser

( )i tAe 3 31 1 2 2 ( )( ) ( )

1 2 3 ...i ti t i tAe A e A e

Laser atom, molecule, cluster,….human?

When all phases are fixed or have fixed relationship, these wavesare called coherent. Otherwise, when the phases are different andhave no correlations, these waves are in random phases.



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)



Recommended Websites for Learning Recommended Websites for Learning QChemQChem

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

• 中文網站可自行搜索關鍵詞：量子化學

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