Lect1 Intro 1

8/2/2019 Lect1 Intro 1

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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.cfm


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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?

Lect1 Intro 1

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