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Physical Chemistry:
Concepts and Applications
Quantum mechanics (21 lectures)
Thermodynamics (17 lectures)Chemical Kinetics (4 lectures)
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All chemistry depends upon the interactions of electrons in
atoms
Electrons are quantum mechanical objects. We cannot
measure their exact positions and momenta
We can, however, obtain the probability distributions of
electrons in atoms, molecules, solids and disordered
materials, from experiment as well as theory
Simple theories of chemical bonding: approximate idea of
electron distributions
Quantum chemistry: how to calculate the electron
distributions and electronic properties of materials
Quantum Mechanical Principles of
Chemical Structure and Bonding
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How do we visualize bonds?
Microscope X-ray diffraction
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Dipole moment: 1.8 D
Bond angle: 104.45 Deg
Bond length: 0.9584 Ang
Lone pairs can
form hydrogen
bonds
How do we get to know H2O?
O
HH H
Covalent
bonds
O
O OH
How do we calculate bond energies?
How do we find the shapes of molecules?
How do we check if VSEPR theory is right?
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Organization
Principles of Quantum Mechanics
Simple, exactly solvable problems
Hydrogen Atom
Many-electron Atoms
Molecules
Books
Atkins, Physical Chemistry Alberty and Silbey, Physical Chemistry
Quiz before Minor I
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Wave-Particle Duality
In classical physics, there is a clear distinction between
waves and particles
The development of quantum mechanics became necessary
in order to explain experiments which suggested that
electromagnetic waves could behave like particles
Classical Particles
Classical Waves
Evidence for particle nature of electromagnetic waves Wave-Particle Duality: The de Broglie Hypothesis
Experiments to verify the wave nature of particles
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Classical Particles
Obey Newtons laws of motion
Characteristic mass: inertial/gravitational mass
In principle, the position and velocity can be specifiedsimultaneously to arbitrary accuracy
Completely predictive or deterministic: If the initial position,
momentum are known and the forces acting on a particle can be
calculated, then the entire trajectory (r(t),v(t)) can be predicted
exactly using Newtons laws
Very successful on a macroscopic scale: planetary orbits,
geostationary satellites, rocket launches
Sometimes works on a molecular scale: kinetic theory of gases
Fdt
xdm =
2
2
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Classical Waves Associated with periodic variations in time and/or space of some
property. Identify time period (frequencies,) or spatial period(wavelengths, )
sound: density
water: surface height (ripples) or density
light: electric and magnetic fields
Require periodic functions to describe waves which must besolutions of special types second-order differential equations 1-dimensional stationary wave equation
3-Dimensional time-dependent wave equation
Interference/Diffraction: Combining periodic functions generatesother periodic functions
Periodicity will be observable if we make measurements on lengthscales less than and time scales less than
2
2
22
2
2
2
2
2
1
dtd
cdzd
dyd
dxd
=++
22
2
kdx
d=
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Experimental Evidence for
Particle Nature of Radiation
Black-body radiation
Photoelectric effect
Compton Effect
Absorption/Emission of Radiation by
Atoms
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The Photoelectric Effect (1905)
Light exists in the formof distinct packets or
quanta of energy, h
An electron can be
ejected from a metal
surface only if a singlequantum of incident
light has energy greater
than the workfunction
of the metal ()
Kinetic energy ofemitted electron =
= hmv2
2
1
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Compton Effect (1923)
The observed shiftin X-raywavelengthIs given by:
Compton could explain this by:
(i) Conservation of energy
where K.E. of electron was calculated
relativistically
(ii) Conservation of momentum
assuming that the X-ray photon
had momentum, p=h/
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Wave-Particle Duality:
The De Broglie Equation (1924)
Expts showed that a photon could have well defined energy as well
as momentum
De Broglie considered the properties of radiation quanta, using the
result from relativity theory that a particle of zero rest mass moving
at velocity c will have momentum p=E/c=h/
By analogy, a non-relativistic particle of mass m and velocity v will
have a wavelength
p
h=Wave property
Particle property
Plancks constant
.
p
h
cE
h
hv
hcc====
/
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Matter WavesPlancks constant determines the length scale on which the wave properties of
particles with non-zero mass become important
How can one generate de Broglie waves of different wavelengths Charged particles can be accelerated through a fixed electrical potential
energy difference Thermal kinetic energy of uncharged particles will also result in a well-
defined wavelength
Jsh 341063.6
=
Particle Kinetic energy (Angstrom)
Electron 1eV 12.2
100eV 1.2
10000eV 0.12
Proton 1 KeV 0.009
1 MeV 28.6 Fermi
1 GeV 0.73 Fermi
Neutron 1.5RT/NA
(Thermal K.E.)
1.5
sin2dn =
Measuring matter waves:Bragg scattering
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Electron Diffraction:
Davisson-Germer Experiment (1927)
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Double-Slit Experiment with a
Single Electron (2006)
www.illuminatingscience.org/2006/10/
Hitachi devised a detector thatcould detect a single electron at
a time with almost 100% efficiency.
The detector would register a signal
only when electron waves would
pass on both sides of the electron
biprism at once.
http://www.hqrd.hitachi.co.jp/em/doubleslit-f2.cfm8/2/2019 Lect1 Intro 1
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Diffraction of small helium clusters
http://www.gwdg.de/~mpisfto/atom_optics_e.html
Question:
Each line is marked by the cluster sizeN. Can you explain the spacing
between lines?