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Bohr model of the Hydrogen Atom
Duality of matter led tothe hypothesis thatelectrons behave aswaves.
Bohr model assumed Only circular orbits
around the nucleus andthat the angular momentum
around the atom must bequantized.
Stable orbital whereconstructive interferenceoccurs.
Destructive interferenceprevents observation oforbits with mismatch ofwaves
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Bohrs Model of the
Hydrogen Atom Bohr concluded:
the energy of the electron in an orbit of hydrogen is
quantized
the energy difference between two orbits must also be
quantized
The frequency of a line in the spectrum corresponds to the
energy difference between two orbits;
Note that this is slightly different than the Einstein equation
for the energy of photons:
E= h
E= h E= h
E= h
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Bohrs Model of the
Hydrogen Atom
The energy of a Bohr orbit(and an
electron in it) is given by
whereRHis theRydberg constant = 2.179 x 10-18 J
En = -RH1
2n
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Hydrogen atom spectra
Visible lines in H atom
spectrum are called the
BALMER series.
Energy
Ultra Violet
Lyman
Infrared
Paschen
Visible
Balmer
En = -2.179x10-18 J
n2
65
3
2
1
4
n
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De Broglie Wave Nature of Matter
E = mc2 Particle behavior E = h Wave behavior Wave and particle behavior
Duality of matter expressed by replacing thespeed of light with the speed of the particle to get called the de Broglie wavelength of any moving
form of matter
mv
h=
mc
h
mc
hc
c
mch
2
2
=
=
==
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De Brogilie WavelengthsParticle or Object Mass (kg) Speed (m/s) de Broglie Wavelength (nm)
Electron 9.109 x 10-31 1.00 x 106 7.27 x 10-1
Proton 1.673 x 10-27 1.00 x 106 3.96 x 10-4
Neutron 1.675 x 10-27 1.00 x 103 3.96 x 10-1
Bullet 1.000 x 10-2 8.00 x 102 8.28 x 10-26
Tennis Ball 5.68 x 10-2 5.00 x 101 2.33 x 10-25
________________________________________________
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Matter - Particles or Waves?
short de Broglie wave
fits within containment
particle properties
observed
long de Broglie wave
exceeds confinement
wave properties
observed
Ugh, this is
outrageous.
Not even one of
us fits in here.
Lets rebel andact like waves
Wow, this is a
great place, lots
of us will fit in
here comfortably.
Lets behave welland act like
particles
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Davisson G.P. Thomson
Davisson, C. J.,
"Are Electrons
Waves?," Franklin
Institute Journal205, 597 (1928)
The Davisson-Germer experiment:
scattering a beam of electrons from
a Ni crystal. Davisson got the 1937
Nobel prize.
At fixed accelerating voltage (fixed
electron energy) find a pattern of sharp
reflected beams from the crystal
At fixed angle, find sharp peaks in
intensity as a function of electron energy
G.P. Thomson performed similar interference
experiments with thin-film samples
i
i
ELECTRON DIFFRACTIONELECTRON DIFFRACTION
The DavissonThe Davisson--GermerGermer experiment (1927)experiment (1927)
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ELECTRON WAVE PROPERTIESELECTRON WAVE PROPERTIES
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X-RAYS AND ELECTRONS WITH THE SAME
WAVELENGTH SHOW IDENTICAL DIFFRACTIONPATTERNS
X-RAYS AND ELECTRONS WITH THE SAME
WAVELENGTH SHOW IDENTICAL DIFFRACTIONPATTERNS
X-Rays Diffracted Electrons Diffracted
LightNo Light
Electrons
No Electrons
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ELECTRON MICROSCOPE
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Electron Micrographs of HIV Virus
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Co
O
Li
The Lithium Ion
Battery Anode
Cobalt Oxide with
Li+
Ions
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Electron Microscopy of LiCoO2
Lithium Ion Rechargeable Batteries
Electron
Micrograph
Computer Simulation
Of LiCoO2 Structure
*Li is the smallest atom
seen in Electron
Microscopy so far
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Inventors of the Scanning Tunneling Microscope
Gerd
BinnigHeinrich
Rohrer
1986 Nobel Prize in Physics for their design of the
scanning tunneling microscope
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Electron Waves in STM
Thick Barrier
Thin Barrier
Tunneling
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The Picture is a kanji symbolthat translates literally asoriginal child. It is used to
represent the atom inscientific translation.
Scanning Tunneling Microscopy
The Symbol is Composed
of About 100 Individual
Iron Atoms on Copper. The
atoms were assembled by
scientists at IBM using a
method known as
Scanning TunnelingMicroscopy (STM).
What does the kanji symbol mean?
What are the red dots that form
the symbol?
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President Clinton today used this tiny map of
the Western Hemisphere created by IBMResearch as a backdrop for hisannouncement of the $497-million NationalNanotechnology Init iative during a speech atthe California Institute of Technology today.Only one-hundredth the diameter of a humanhair, this map was made by a scanningtunneling microscope that deposited smallclusters of gold atoms to form each dot.Nanotechnology is the science of controllingmatter at the atomic scale.
San Jose, Calif. (January 21, 2000) --
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Uncertainty PrincipleUncertainty PrincipleUncertainty PrincipleProblem of defining nature of
electrons in atoms solved by W.
Heisenberg.Cannot simultaneously define the
position and momentum (= mv)
of an electron.x p = h
At best we can describe the
position and velocity of anelectron by a
PROBABILITY DISTRIBUTION
W. Heisenberg
1901-1976
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Uncertainty Principle
24
h
px
h
=
m2vx h
p=mv
Position, x and
momentum, p
Position, xand
Velocity, v
p= mv, m is constant
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Trying to measure the pathway of
an electronElectron
Velocity
Photon
Y
X
h
h
h
h
h
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Where is the electron in an atom?Where is the electron in an atom?
v = 1 x 106 m/s
h
v = 106 0.29 x 106 m/sx = 0.1 nm
Calculate the
uncertainty
in the position of the
electron after a time
period of 1 ms (10-3s) after the initial
measurement
The Heisenberg Viewpoint
x = vt
x = vt
x = (.58 x 106 m/s)(10-3 s)
x = 580 m
The de Broglie Viewpoint
( )( )nm727.0m10x27.7
s/m10x1kg10x109.9
sJ10x626.6
mv
h
10
631
34
=
=
?
. .Where will I be in
one millisecond ?
Electron confined to region <
will act like a wave The uncertainty inposition rapidly increases
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Schrodinger applied idea of e-
behaving as a wave to the problemof electrons in atoms.
Solution to WAVE EQUATION givesset of mathematical expressions
called
WAVE FUNCTIONS,Each describes an allowed energy
state of an e-
Quantization introduced naturally.
E.E. SchrodingerSchrodinger
18871887--19611961
Wave MechanicsWave MechanicsWave Mechanics
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WAVE FUNCTIONS, WAVE FUNCTIONS,WAVE FUNCTIONS, is a function of distance and twois a function of distance and two
angles.angles.
For 1 electron,For 1 electron, corresponds to ancorresponds to anORBITALORBITAL the region of spacethe region of spacewithin which an electron is found.within which an electron is found.
does NOT describe the exactdoes NOT describe the exactlocation of the electron.location of the electron.
22 is proportional to the probabilityis proportional to the probabilityof finding an eof finding an e-- at a given point.at a given point.
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Quantum Numbers (QN)Quantum Numbers (QN)- Application of wave mechanics or the Schrdingerequation yielded energies for the electrons that
agreed well with the experimental data.
- The Schrdinger equation yields three quantumnumbers (QN) which define electron energies betterthan did the Bohr theory.
- Quantum mechanics does not allow us to describethe e- in an atom as moving in an orbit, but it doesallow us to make statistical statements about e-
density.
- We need to know these QN and how they define theorbital.
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Orbital energies of the hydrogen atom.
Schrdinger Result Bohr Result22
42en
n2
eZmEh
=
(Note Scale Break Here)
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