quantum theory micro-world macro-world lecture 14
Post on 19-Dec-2015
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Quantum Theory
Micro-world Macro-worldLecture 14
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Light propagates like a wave,& interacts as a particle
E=hf
hp =
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Louis deBroglie
If light behaves as particles, maybe other “particles” (such as electrons) behave as waves h
p = Photons:
hp =
particles:
hp =
Wave-particle duality is
a universal phenomenon
“deBroglie
wavelength”
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Ordinary-sized objects have tiny wavelengths
0.2kg30m/s
hp =
hmv
= 6.6x10-34Js
0.2kg x 30 m/s =
6.6x10-34Js6.0 kg m/s = 1.1x10-34m =
Incredibly small
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the wavelength of an electronis not so small
9x10-31 kg 6x106 m/s
hp =
hmv
= 6.6x10-34Js
9x10-31kg x 6x106 m/s =
6.6x10-34Js5.4x10-24 kg m/s = 1.2x10-10m =
-
About the size of an atom
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Send low-momentum electrons thru narrow slits
See a diffraction pattern characteristic of
wavelength =h/p as predicted by de Broglie
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or through a small hole
“Diffraction”rings
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Matter waves(electrons through a crystal)
“Diffraction”rings
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Electron waves through a narrow slit acquire some py
py
py
y
x
y
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Waves thru a narrower slit
wider
py
py
y
When the slit becomes narrower, thespread in vertical momentum increases
x
y
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y/2
x
y
/2
hyp
hyp
yp
h
yph
y
y
sin2
2sin
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Heisenberg Uncertainty Principle
y py > h
Uncertaintyin location
Uncertainty in
momentum in
that direction
If you make one of these smaller, the other has to become bigger
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Heisenberg tries to measure the location of an atom
For better precision, usea shorter wavelength
But then the momentumchange is higher
x px > h
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Localize a baseball
0.2kg x px > h px > hx
Suppose x= 1x10-10m
px > 6.6x10-34Js
1x10-10m
vx >
= 6.6x10-24kgm/s
A very tiny uncertainty
About the size of a single atom
px m
6.6x10-44Js
0.2kg = = 3.3x10-23 m/s
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Localize an electron
x px > h px > hx
Suppose x= 1x10-10m
px > 6.6x10-34Js
1x10-10m
vx >
= 6.6x10-24kgm/s
Huge, about 2% of c
About the size of a single atom
px me
6.6x10-24Js
9x10-31kg = = 7x106 m/s
-me=9x10-31kg
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uncertainty is inherentin the quantum world
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The Bohr-Rutherford Atom
Physics 100
Chapt 23
Nils Bohr
Ernest Rutherford
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1895 J.J. Thomson discovered electron
+-
- -
-
+ +
+ +
cathode
anode
“cathode rays”
Vacuum flask
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Cathode rays have negative chargeand very small mass
+-
- -
-
+ +
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cathode
anode N
S
m=0.0005MHydrogen
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Plum pudding?
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10-10m
+
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Positively chargedporridge
Negatively chargedraisins (plums)
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Planetary-like?
10-10m
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Positively chargeddense central nucleus
Negatively chargedorbiting electrons
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Rutherford Experiment
Vacuumflask
-rays
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What’s in the box?
Is all the mass spreadthroughout as in a box
of marshmallows”?
or is all the massconcentrated in a dense
“ball-bearing”?
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Figure it out without opening (or shaking)
Shoot bullets randomly through the box. If it is filled with marshmallows, all the bullets will go straight through without (much) deflection
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Figure it out without opening (or shaking)
If it contains a ball-bearing most the bullets will go straight through without deflection---but not all
Occasionally, a bullet will collide nearly head-on to the ball-bearing and be deflected by a large angle
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Rutherford used -ray “bullets” to distinguish between the plum-pudding & planetary models
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no way for -rays to scatter at wide angles
Plum-pudding:
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+
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Occasionally, an-rays will be pointed head-on to a nucleus & will scatter at a wide angle
distinguishing between the plum-pudding & planetary models
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Rutherford saw ~1/10,000a-rays scatter at wide angles
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from this he inferred a nuclearsize of about 10-14m
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Rutherford atom
+10-14m
10-10m
Not to scale!!!If it were to scale,the nucleus wouldbe too small to seeEven though it has more than 99.9% of the atom’s mass
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Relative scalesAloha stadium
Golf ball
AtomNucleus
99.97% of the mass
x10-4
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Classical theory had trouble with Rutherford’s atom
Orbiting electrons are accelerating
Accelerating electrons should radiate light
According to Maxwell’stheory, a Rutherford
atom would only survivefor only about 10-12 secs
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Fraunhofer discovered that some wavelengths aremissing from the sun’s black-body spectrum
sola
Other peculiar discoveries:
Solar light spectrum:
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Other discoveries…Low pressure gasses, when heated,
do not radiate black-body-like spectra;instead they radiate only a few specific colors
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bright colors from hydrogen match the missing colors in sunlight
Hydrogen spectrum
Solar spectrum
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Bohr’s idea
“Allowed”orbits
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Hydrogen energy levels
+1
3
4
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Hydrogen energy levels
+
1
2
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What makes Bohr’s allowed energy levels allowed?
Recall what happens when we force waves into confined spaces:
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Confined waves
Only waves with wavelengths that just fit in survive(all others cancel themselves out)
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Electrons in atoms are confined matter waves ala deBroglie
This wave, as it goes around, will interferewith itself destructively and cancel itself out
However, if the circumference is exactly an integer number of wavelengths, successive
turns will interfere constructively
Bohr’s allowed energy states correspond to thosewith orbits that are integer numbers of wavelengths
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Bohr orbits
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Bohr orbits
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Quantum Mechanics
Erwin Schrodinger
Schrodinger’s equation
ExV
dx
d
m )(
2 2
222h
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Matter waves are “probability” waves
Probability to detect theelectron at some place
is 2 at that spot
Electrons are most likely
to be detected hereor here
Electrons will never be detected here
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Electron “clouds” in Hydrogen
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Nobel prizes for Quantum Theory
1918 Max Planck E=hf1921 Albert Einstein photons1922 Niels Bohr atomic orbits1929 Louis de Broglie matter waves1932 Werner Heisenberg uncertainty principle…