Transcript Physical Chemistry 2nd Edition

Chapter 12
From Classic to Quantum Mechanics
Physical Chemistry 2nd Edition
Thomas Engel, Philip Reid
Objectives
• Introduction of Quantum Mechanics
• Understand the difference of classical theory
and experimental observations of quantum
mechanics
Chapter 12: From Classic to Quantum Mechanics
Physical Chemistry 2nd Edition
© 2010 Pearson Education South Asia Pte Ltd
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
Chapter 12: From Classic to Quantum Mechanics
Physical Chemistry 2nd Edition
© 2010 Pearson Education South Asia Pte Ltd
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.
Chapter 12: From Classic to Quantum Mechanics
Physical Chemistry 2nd Edition
© 2010 Pearson Education South Asia Pte Ltd
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.
Chapter 12: From Classic to Quantum Mechanics
Physical Chemistry 2nd Edition
© 2010 Pearson Education South Asia Pte Ltd
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.
Chapter 12: From Classic to Quantum Mechanics
Physical Chemistry 2nd Edition
© 2010 Pearson Education South Asia Pte Ltd
12.3 Blackbody Radiation
•
Under the condition of equilibrium between the
radiation field inside the cavity and the glowing
piece of matter,
8v 2
pv, T dv  3 EOSC dv
c
where v = frequency
ρ = spectral density
T = temperature
c = speed of light
EOSC = average energy of an oscillating dipole in the
solid
Chapter 12: From Classic to Quantum Mechanics
Physical Chemistry 2nd Edition
© 2010 Pearson Education South Asia Pte Ltd
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.
Chapter 12: From Classic to Quantum Mechanics
Physical Chemistry 2nd Edition
© 2010 Pearson Education South Asia Pte Ltd
12.3 Blackbody Radiation
•
Max Planck derived the agreement between
theory and experiment on radiation energy.
E  nhv
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.
Chapter 12: From Classic to Quantum Mechanics
Physical Chemistry 2nd Edition
© 2010 Pearson Education South Asia Pte Ltd
12.3 Blackbody Radiation
•
Introducing some classical physics, Max Planck
obtained the following relationship:
EOSC 
•
hv
e hv / kT  1
A more general formula for the spectral
radiation density from a blackbody is obtained.
8hv 3
1
pv, T  
dv
3
hv / kT
c e
1
Chapter 12: From Classic to Quantum Mechanics
Physical Chemistry 2nd Edition
© 2010 Pearson Education South Asia Pte Ltd
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.
Chapter 12: From Classic to Quantum Mechanics
Physical Chemistry 2nd Edition
© 2010 Pearson Education South Asia Pte Ltd
12.4 The Photoelectric Effect
•
Albert Einstein states that the energy of light,
E  v
•
where β = constant
v = frequency
From energy conservation the energy of the
electron, Ee, is
Ee  v  
where Ф = work function
Chapter 12: From Classic to Quantum Mechanics
Physical Chemistry 2nd Edition
© 2010 Pearson Education South Asia Pte Ltd
12.4 The Photoelectric Effect
•
The results of β is identical to Planck’s constant,
h, thus
E  hv
Chapter 12: From Classic to Quantum Mechanics
Physical Chemistry 2nd Edition
© 2010 Pearson Education South Asia Pte Ltd
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.
Chapter 12: From Classic to Quantum Mechanics
Physical Chemistry 2nd Edition
© 2010 Pearson Education South Asia Pte Ltd
Solution
We write Ee  hv    hc /     and convert the units
of  from electron-volts to joules:
  2.26eV 1.602 1019 J / eV   3.62 1019 J
Electrons will only be ejected if the photon energy,
hv, is greater than  . The photon energy is
calculated to be
hc

6.626 10 2.998 10   6.62 10

34
300 10
8
9
which is sufficient to eject electrons.
Chapter 12: From Classic to Quantum Mechanics
Physical Chemistry 2nd Edition
© 2010 Pearson Education South Asia Pte Ltd
19
J
Solution
We can obtain
Using
Ee  hc /      2.99 10 19 J
Ee  1 / 2mv2
.
, we calculate that


2 Ee
2 2.99 10 19 J
5
v


8
.
10

10
m/ s
31
m
9.109 10
Chapter 12: From Classic to Quantum Mechanics
Physical Chemistry 2nd Edition
© 2010 Pearson Education South Asia Pte Ltd
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
h

p
where p = mv (particle momentum)
Louis-Victor-Pierre-Raymond, 7th duc de Broglie
Chapter 12: From Classic to Quantum Mechanics
Physical Chemistry 2nd Edition
© 2010 Pearson Education South Asia Pte Ltd
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
E


34 2
p
h
6.626 10
18



2
.
7

10
or 17eV
2
31
10
2m 2m
2 9.109 10
3.0 10
2
2

Chapter 12: From Classic to Quantum Mechanics
Physical Chemistry 2nd Edition
© 2010 Pearson Education South Asia Pte Ltd


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.
Chapter 12: From Classic to Quantum Mechanics
Physical Chemistry 2nd Edition
© 2010 Pearson Education South Asia Pte Ltd
12.6 Diffraction by a Double Slit
•
For diffraction of light from a thin slit, b >> a.
Chapter 12: From Classic to Quantum Mechanics
Physical Chemistry 2nd Edition
© 2010 Pearson Education South Asia Pte Ltd
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.
Chapter 12: From Classic to Quantum Mechanics
Physical Chemistry 2nd Edition
© 2010 Pearson Education South Asia Pte Ltd
12.6 Diffraction by a Double Slit
•
The condition that the minima satisfy is
n
sin  
, n  1,2,3,.....
a
where λ = wavelength
•
12.4 Diffraction from Double Slit
Chapter 12: From Classic to Quantum Mechanics
Physical Chemistry 2nd Edition
© 2010 Pearson Education South Asia Pte Ltd
12.6 Diffraction by a Double Slit
•
For double-slit diffraction experiment,
Light and electron diffraction:
http://physics-animations.com/Physics/English/top_ref.htm#elin
Chapter 12: From Classic to Quantum Mechanics
Physical Chemistry 2nd Edition
© 2010 Pearson Education South Asia Pte Ltd
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.
Chapter 12: From Classic to Quantum Mechanics
Physical Chemistry 2nd Edition
© 2010 Pearson Education South Asia Pte Ltd
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, 1/   v~ of all lines in an atomic
hydrogen spectrum is given by
•
1
1
1  1
~
v cm  RH cm  2  2 , n  n1
 n1 n 




Chapter 12: From Classic to Quantum Mechanics
Physical Chemistry 2nd Edition
© 2010 Pearson Education South Asia Pte Ltd
Example 12.3
Calculate the radius of the electron in H in its
lowest energy state, corresponding to n =1.
Solution:
We have


40 h 2 n 2 4  8.85419 10 12  1.0555 10 34 12
r

2
31
19 2
me e
9.109 10  1.6022 10

 5.292 10 11 m
Chapter 12: From Classic to Quantum Mechanics
Physical Chemistry 2nd Edition
© 2010 Pearson Education South Asia Pte Ltd

Random phase, coherent wave and laser
  Ae
  A1e
i (1t 1 )
 A2e
i (t  )
i (2t 2 )
 A3e
i (3t 3 )
 ...
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.
Chapter 12: From Classic to Quantum Mechanics
Physical Chemistry 2nd Edition
© 2010 Pearson Education South Asia Pte Ltd
Laser atom, molecule, cluster,….human?
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)
Chapter 12: From Classic to Quantum Mechanics
Physical Chemistry 2nd Edition
© 2010 Pearson Education South Asia Pte Ltd
Recommended Websites for Learning QChem
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
Chapter 12: From Classic to Quantum Mechanics
Physical Chemistry 2nd Edition
© 2010•Pearson
Education South Asia Pte Ltd
中文網站可自行搜索關鍵詞：量子化學