Download Lecture 37 - USU Department of Physics

Physics of Technology
PHYS 1800
Lecture 37
Introduction
Quantum Mechanics
in a Day
Section 0
Lecture 1
Slide 1
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Quantum Mechanics
Lecture 37 Slide 1
PHYSICS OF TOF
ECHNOLOGY
- PHYS 1800
PHYSICS
TECHNOLOGY
ASSIGNMENT SHEET
Spring 2009Spring
Assignment
Sheet
2009
Date
Day
Lecture
Chapter
Feb 16
M
Presidents Day
17
Tu
Angular Momentum (Virtual Monday)
18
W
Review
19
H
Test 2
20
F*
Static Fluids, Pressure
Feb 23
M
Flotation
25
W
Fluids in Motion
27
F*
Temperature and Heat
Mar 2
M
First Law of Thermodynamics
4
W
Heat flow and Greenhouse Effect
6
F*
Climate Change
Mar 9-13
M-F
Spring Break
Mar 16
M
Heat Engines
18
W
Power and Refrigeration
20
F*
Electric Charge
Mar 23
M
Electric Fields and Electric Potential
25
W
Review
26
H
Test 3
27
F*
Electric Circuits
Mar 30
M
Magnetic Force Review
Apr 1
W
Electromagnets
3
F
Motors and Generators
Apr 6
M
Making Waves
8
W
Sound Waves
10
F*
E-M Waves, Light and Color
Apr 13
M
Mirrors and Reflections
Introduction
Section
0 Lecture 1 Slide 2
15
W
Refraction and Lenses
17
F*
Telescopes and Microscopes
Apr 20
M
Review
22
W
Seeing Atoms
24
F
The really BIG & the really small
INTRODUCTION TO Modern Physics PHYX 2710
May
1
F
Final Exam: 09:30-11:20am
No Class
8
5-8
5-8
9
9
9
10
10
10
No Classes
11
11
12
12
13
9-12
13
14
9-12
14
15
15
16
17
17
17
1-17
18 (not on test)
21 (not on test)
Homework Due
-
6
7
8
-
9
10
11
No test week
12
Fall 2004
* = Homework Handout
*Homework Handout
Physics of Technology—PHYS 1800
Spring 2009
Quantum Mechanics
Lecture 37 Slide 2
Interference
Young’s Double Slit
experiment
X 1  X 2  n , n  0,1,2...
D
 yn  n
d
You must add
amplitudes
E,
Introduction
not powers P
(intensities)
Section 0
Lecture 1
Slide 3
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Quantum Mechanics
Lecture 37 Slide 3
Interference of Light Waves
Is light a wave or a particle?
– If it is a wave, it should exhibit interference effects:
Recall that
two waves can
interfere
constructively
or
destructively
Introduction
depending on
their phase.
Section 0
Lecture 1
Slide 4
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Quantum Mechanics
Lecture 37 Slide 4
Light from a single slit is split by passing through two slits,
resulting in two light waves in phase with each other.
The two waves will interfere constructively or destructively,
depending on a difference in the path length.
If the two waves travel equal distances to the screen, they interfere
constructively and a bright spot or line is seen.
Introduction
Section 0
Lecture 1
Slide 5
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Quantum Mechanics
Lecture 37 Slide 5
If the distances traveled differ by half a wavelength, the two waves
interfere destructively and a dark spot or line appears on the screen.
If the distances traveled differ by a full wavelength, the two waves
interfere constructively again resulting in another bright spot or line.
The resulting interference pattern of alternating bright and dark
lines is a fringe pattern.
y
path difference  d
x

Introduction
Section 0
Lecture 1
Slide 6
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Quantum Mechanics
Lecture 37 Slide 6
Similarly, interference can occur when light waves are reflected from the
top and bottom surfaces of a soap film or oil slick.
The difference in the path length of the two waves can produce an
interference pattern.
This is called
thin-film
interference.
Introduction
Section 0
Lecture 1
Slide 8
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Quantum Mechanics
Lecture 37 Slide 8
Different wavelengths of light interfere constructively or
destructively as the thickness of the film varies.
This results in the many different colors seen.
Introduction
Section 0
Lecture 1
Slide 9
INTRODUCTION TO Modern Physics PHYX 2710
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Spring 2009
Quantum Mechanics
Lecture 37 Slide 9
The thin film may also be air between two glass plates.
Each band represents a different thickness of film.
Introduction
Section 0
Lecture 1
Slide 10
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Quantum Mechanics
Lecture 37 Slide 10
Diffraction and Gratings
The bright fringes in a double-slit interference
pattern are not all equally bright.
– They become less bright farther from the center.
– They seem to fade in and out.
This effect, called diffraction, is due to interference
of light coming from different parts of the same slit
or opening.
Introduction
Section 0
Lecture 1
Slide 11
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Quantum Mechanics
Lecture 37 Slide 11
Diffraction
For constructive interference:
Path Difference  d sin( )  n ,
n  0,1,2...
Introduction
Section 0
Lecture 1
Slide 15
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Quantum Mechanics
Lecture 37 Slide 15
The diffraction pattern produced by a square opening
has an array of bright spots.
Looking at a star or distant street light through a window
screen can produce a similar diffraction pattern.
Introduction
Section 0
Lecture 1
Slide 16
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Quantum Mechanics
Lecture 37 Slide 16
X-Ray Diffraction
Introduction
Section 0
Lecture 1
Slide 17
INTRODUCTION TO Modern Physics PHYX 2710
Braggs’s Law: nλ=2d sin(Θ)
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Quantum Mechanics
Lecture 37 Slide 17
Why study everyday phenomena?
The same physical principles that govern our
everyday experiences also govern the entire
universe
– A bicycle wheel, an atom, and a galaxy all operate
according to laws for angular momentum.
Introduction
Section 0
Lecture 1
Slide 18
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Quantum Mechanics
Lecture 37 Slide 18
What are the major subfields in Physics?
Classical Physics (pre 20th century)
–
–
–
–
Mechanics → forces, motion
Thermodynamics → heat, temperature
Electricity and magnetism → charge, currents
Optics → light, lenses, telescopes
Modern Physics (20th century)
– Atomic and nuclear
→ radioactivity, atomic power
– Quantum mechanics
} → basic structure matter
– Particle
physics
Introduction Section 0 Lecture 1 Slide 19
– Condensed matter → solids and liquids, computers,
lasers
– Relativity, Cosmology → universe, life!
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Quantum Mechanics
Lecture 37 Slide 19
State of Physics cira 1895
Conservation Laws
Electricity & Magnetism • Energy
Statistical Mechanics
• 3 Laws of Thermodynamics
• Kinetic Theory
Maxwell Equations (c 1880)
• Gauss’ Law
•Faraday’s Law
•Ampere’s Law
•No magnetic monopoles
• Linear & Angular Momentum
Mechanics (Gravity)
Newton’s Laws (c 1640)
1-Law of inertia
2-F=ma
3-Equal and opposite reactions
Introduction
Section 0
Lecture 1
Slide 20
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Quantum Mechanics
Lecture 37 Slide 20
Limits of pre-Modern Physics
Dimension Range of
Applicability
Range of Application
Length
10-6 to 10+8 m
Smoke particle (Brownian
Motion) to the solar system
Mass
10-9 to 10+31 kg
Dust particles to solar mass
Time
10+10 to 10+17 sec-1
10-3 to 10+9 sec
Microwave to UV light
Smallest timing increments
(msec) to celestial motions
(centuries)
Lecture 1
-6 to 010+5
10Section
m/s
Small particles to celestial
motion
Velocity
Introduction
Slide 21
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Quantum Mechanics
Lecture 37 Slide 21
Then All Hell Broke Lose
“Thirty Years That Shook Physics”
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
1887 Michelson-Morley exp. debunks “ether”
1895 Rontgen discovers x rays
1897 Becquerel discovers radioactivity
1897 Thomson discovers the electron
1900 Planck proposes energy quantization
1905 Einstein proposes special relativity
1915 Einstein proposes general relativity
1911 Rutherford discovers the nucleus
1911 Braggs and von Laue use x rays to determine crystal structures
1911 Ones finds superconductors
1913 Bohr uses QM to explain hydrogen spectrum
1923 Compton demonstrates particle nature of light
1923 de Broglie proposes matter waves
1925 Davisson & Germer prove matter is wavelike
1925 Heisenberg states uncertainty principle
1926 Schrodinger
develops
wave equation
Introduction Section
0 Lecture
1 Slide 22
1924-6 Boson and Fermion distributions developed
•
1949 Murphy's Law stated
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Quantum Mechanics
Lecture 37 Slide 22
Current State of Physics cira 2009
Conservation Laws
Statistical Mechanics
•
•
•
Electricity & Magnetism •
• Physics of many particles
• Fermions and Bosons
• Partitioning of Energy
• Thermodynamics
• Time and Entropy
Energy
Linear & Angular Momentum
Charge, Spin
Lepton and Baryon Number
Maxwell Equations (c 1880)
Weinburg-Salom Model
• QED
• Unites E&M, Weak NF
Mechanics (Gravity)……
Weak Nuclear Force
General Relativity
Space and time
Radioactivity
Standard Model
Quantum Mechanics
Introduction
Section 0
•Schrodinger/Dirac
Equation
•Probabilistic approach
Lecture 1
Slide 23
• QCD
• Unites E&M, Strong NF, Weak NF
Strong Nuclear Force
INTRODUCTION TO Modern Physics PHYX 2710
Composition of subatomic particles
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Quantum Mechanics
Lecture 37 Slide 23
Limits of Current Modern Physics
Dimension Range of
Applicability
Range of Application
Length
10-18 to 10+26 m
Quark size to the universe size
Mass
10-31 to 10+40 kg
Electrons to galactic clusters
Time
10+3 to 10+22 sec-1
10-16 to 10+17 sec
Radio to Gamma rays
Sub-femtosecond
spectroscopy to age of
universe
Velocity
10-8 to 10+8 m/s
Introduction
Section 0
Lecture 1
Slide 24
Sub-atomic particles to speed
of light
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Quantum Mechanics
Lecture 37 Slide 24
Cathode rays, Electrons, and X-rays
By the end of the nineteenth century, chemists
were using the concept of atoms to explain their
properties.
Physicists were less convinced.
– The discovery of cathode rays was the beginning of
atomic physics.
Two electrodes are sealed in a glass tube.
As the tubeIntroduction
is evacuated,
a glow discharge
Section 0 Lecture 1 Slide 25
appears in the gas between the electrodes.
With further evacuation, the discharge
disappears, and a glow appears on the end
of the tube opposite the cathode.
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Quantum Mechanics
Lecture 37 Slide 25
An invisible radiation seemed to emanate from
the cathode to produce the glow on the
opposite wall of the tube.
– The invisible radiation was called cathode rays.
If the north pole of a magnet is brought down
toward the top of a cathode-ray tube, the spot
of light is deflected to the left across the face of
the tube.
– This indicates the cathode rays are negatively
charged particles.
Two electrodes are sealed in a glass
tube.
As the tube is evacuated, a glow
Introduction
Section
Lecture 1
discharge appears
in the
gas0 between
the electrodes.
Slide 26
With further evacuation, the discharge
disappears, and a glow appears on the
end of the tube opposite the cathode.
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Quantum Mechanics
Lecture 37 Slide 26
J. J. Thomson used both electric fields and magnetic
fields to deflect the beam.
The combined effect allowed him to estimate the velocity of
Introduction Section 0 Lecture 1 Slide 27
the particles.
With the deflection produced by the magnetic field alone, this
allowed him to estimate the mass of the particles.
– We now call these particles electrons.
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Quantum Mechanics
Lecture 37 Slide 27
You probably use cathode rays almost every
day.
The heart of most television sets is the
cathode ray tube, or CRT.
Introduction
Section 0
Lecture 1
Slide 28
Do you
know how
a TV
works?
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
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Spring 2009
Quantum Mechanics
Lecture 37 Slide 28
The electrodes that produce and focus the electron beam are called the
electron gun.
– An electric current passes through the filament to heat the cathode to emit
electrons.
– Electrons are accelerated from the cathode to the anode by the high
voltage.
– Electrons passing through the hole in the anode make up the electron
beam.
After leaving the electron gun, the
beam of electrons travel across the
tube, producing a bright spot of
light when it strikes the glass face
of the tube.
Magnets deflect the beam so that it
strikes different points on the face
of the tube at different times.
Section 0 Lecture 1 Slide
The beamIntroduction
scans across
the entire
face of the tube in a fraction of a
second, to form the picture.
29
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Quantum Mechanics
Lecture 37 Slide 29
Experiments on the “New”Particle”
The Electron
Introduction
Section 0
Lecture 1
Slide 30
Robert Millikan measured the
quantized charge on the electron
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
J.J. Thomson measured the
charge-to-mass ratio e/m
Quantum Mechanics
Lecture 37 Slide 30
Davisson and Germer Experiment
In 1927 Davisson and Germer
For electrons:
first demonstrated the
diffraction patterns generated
h
1.226

nm
by electrons of 10eV passing  
2mE
eV
through a Ni crystal.
Introduction
Section 0
Lecture 1
Slide 31
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Quantum Mechanics
Lecture 37 Slide 31
Electron Diffraction
Energy Electron Diffraction:
Electron and x-ray both
exhibit diffraction from
crystals.
Introduction
Section 0
Lecture 1
Slide 32
INTRODUCTION TO Modern Physics PHYX 2710
Braggs’s Law: nλ=2d sin(Θ)
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Quantum Mechanics
Lecture 37 Slide 32
Electron Interference
Introduction
Section 0
Lecture 1
Electron Single Slit
Interference: Effects are
clearly observed. However,
as soon as “electron
tracking” is instituted, the
interference pattern
disappears!
Slide 33
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
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Spring 2009
Quantum Mechanics
Lecture 37 Slide 33
Low Energy Electron Diffraction
Typical LEED systems. (left) UHV
surface analysis chamber. (right)
LEED electron guns and grids.
Introduction
Section 0
Lecture 1
Slide 34
Low Energy Electron Diffraction is a standard tool in surface
science. ~50 eV electrons with λ~1 Å are diffracted from surface
atoms to determine atomic structure.
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Quantum Mechanics
Lecture 37 Slide 34
LEED Images
A SPA LEED image of
silicon taken with 128 eV
electrons.
Introduction
Section 0
Lecture 1
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Slide 35
The organic molecule PTCDI
adsorbed on the 110 surface
of Ag.
Quantum Mechanics
Lecture 37 Slide 35
Neutron Diffraction
Section 0 Lecture 1 Slide 36
(left) TripleIntroduction
axis neutron
diffractometer
at the NIST Neutron scattering facility.
(right) Diffraction pattern from
nuetrons.
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Quantum Mechanics
Lecture 37 Slide 36
...even
Quantum
Physics
(matter
waves)...
Introduction
Section 0
Lecture 1
Slide 37
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Quantum Mechanics
Lecture 37 Slide 37
Nobel Prizes Related to Wave-Particle Duality
There have been 14 Nobel Prizes in physics
awarded that have some direct relation to
the wave-particle duality. Albert Einstein
received the Nobel Prize for one of these,
the photoelectric effect.
Introduction
Section 0
Lecture 1
Slide 38
Annotated list of winners.
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Quantum Mechanics
Lecture 37 Slide 38
Pioneers in the Wave Theory of Particles
Introduction
Section 0
Lecture 1
Born
Slide 39
Heisenburg
Schrodinger
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
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Spring 2009
Quantum Mechanics
Lecture 37 Slide 39
Particles as a Wave
In 1924 de Broglie suggested that electrons
may have wave properties. The wave length
of an electron is proposed to be h/p where p
is the momentum of the electron.
De Broglie waves:
• This expression is consistent with
photon (E=pc) or p=h/ λ.
h
h



p photon
p particle  mv
• Because of the Planck constant,
the λ of macroscopic object is not
detectable.
• Lower momentum particle is more
wavelike. Introduction Section 0 Lecture 1 Slide
h
For electrons:
40

• Higher energy wave is more
particle like.
h
1.226

nm
2mE
E
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Quantum Mechanics
Lecture 37 Slide 40
De Broglie Wave Problems
Assume the mass of the jelly bean is 5 g and its
velocity is 1 m/s. The total energy is just the
kinetic energy E=KE=1/2 mv2 .
2
p
Then E 
 1 102 J  6 1016 eV
What is the
de wave
length of a
jelly bean?
2m
  h p  6 1032 m !
And
What is the de
Broglie wave
length of a
Germer Introduction
electron?
For an electron all the electrostatic PE is
converted to KE, eV  1/2 mv2 . First solve for p
then for λ.
Section 0
Lecture 1
First
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Then
Physics of Technology—PHYS 1800
Spring 2009
Slide 41 2
p
 8 1018 J  50 eV
2m
  h  6 1010 m !
E  eV 
p
Quantum Mechanics
Lecture 37 Slide 41
Waves of what?
The physical interpretation of de Broglie waves
(the wave function or Schrodinger waves) is
related to the probability of finding a moving
particle at a particular location (x,y,z) and time t.
• Because Ψ(x,y,z,t) is complex and can be
positive or negative, it cannot be the probability
directly.
Born
• | Ψ(x,y,z,t) |2 is the probabilityof finding the
particle at location (x,y,z) at time t.
Introduction
Section 0
Lecture 1
Slide 42
• To be a probability function, it must obey a
normalization condition 2stating it must be
( x, y, z) dV  1
somewhere:

INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Schrodinger
Physics of Technology—PHYS 1800
Spring 2009
Quantum Mechanics
Lecture 37 Slide 42
The Schrödinger Equation
 2  2   x, t 
 x, t 




U
(
x
)

x
,
t

i

2m x 2
t
The Schrodinger
Wave equation:
U(x): Potential Energy
P   ( x, t )

2
 ( x, t ) :Complex wave function
probability to find the particle at (x,t)

 ( x, t ) dx   ( x) dx 1 normalization of the
2
2
wave function
 ( x, t )  ( x, t )
 ( x, t ),
, must be continuous
,
x
Let
Introduction
Sectioni0t
( x, t )   ( x)e
t
Lecture 1
2
 43d
Slide

 x 
2
2m dx
2
 U ( x) x    x 
2
2

d
 x 
Time independent Schrödinger equation 
 U ( x) x   E x 
2
2m dx
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Quantum Mechanics
Lecture 37 Slide 43
Matter is made up of atoms…
The Atomic Theory, a cornerstone of
modern science, was proposed by
an early Greek thinker,
Democritus (c.460 BC - c.370
BC).
2400 year later, Feynman deemed
this the most important notion in
science
Introduction
Section 0
Lecture 1
Slide 44
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
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Spring 2009
Quantum Mechanics
Lecture 37 Slide 44
Trying to see atoms…
Optical image
STM Image
(5 X mag)
(3,000,000 X
mag)
SEM Image
STM Image
(300,000 X
mag)
(24,000,000
mag)
Introduction
Section 0
Lecture 1
Slide 45
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Magnified images of semiconductor chip.
Physics of Technology—PHYS 1800
Spring 2009
Quantum Mechanics
Lecture 37 Slide 45
Seeing atoms…finally!!!
Introduction
Section 0
Lecture 1
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Atomic scale images
seen with scanning
tunneling
microscope
STM developed in
1985 at IBM
Measures extent of
electron cloud
Slide 46
Binnig and Roher’s original STM
Quantum Mechanics
Lecture 37 Slide 46
Examples of STM images…
Pt (100) with
vaccancies
Si (111) 7x7
reconstructi
on
Introduction
Section 0
Annealed
decanethiol
Lecture 1 Slide 47
film on
Au(111)
INTRODUCTION TO Modern Physics PHYX 2710
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Physics of Technology—PHYS 1800
Spring 2009
Si (111) with
Quantum Mechanics
terraces
and
Lecture 37 Slide 47
Examples of STM images (part 2)…
Introduction
Section 0
Lecture 1
Slide 48
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Quantum Mechanics
Lecture 37 Slide 48
Barrier Penetration (QuantumTunneling)
V(x)
V ( x)  Vo
V0
E
0
0
a
,0 xa
Ψ is damped
, otherwise
Ψ oscillates
x
There is a certain probability T that the particle can tunnel
through the barrier,
a
T Introduction
 e 0
 2 k ( x ) dx
 2 ka
Lecture
e 1
Section 0
where
Slide 49
k
2mV ( x)  E 

The thicker or higher the barrier, the less the tunneling
probability  approaches classical result
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
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Spring 2009
Quantum Mechanics
Lecture 37 Slide 49
How an STM works…
• An STM s a glorified
phonograph needle
• Tip motion uses
piezioelectric crystals
• Tunneling current
results from overlap of
electron wavefunction
with conducting
surface
Introduction
Section 0
Lecture 1
Slide 50
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Quantum Mechanics
Lecture 37 Slide 50
How an STM works (part 2)…
Introduction
Section 0
Lecture 1
Slide 51
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Quantum Mechanics
Lecture 37 Slide 51
Corralling electrons…
Introduction
Section 0
Lecture 1
Slide 52
STM used to make direct
maps of the Quantum
Mechanicsl
probability
distribution
of
the
electron wave function of
2D state confined by
“corrals”
made
of
adsorbed atoms.
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Quantum Mechanics
Lecture 37 Slide 52
Corralling electrons…
Introduction
Section 0
Lecture 1
Slide 53
STM used to make direct
maps of the Quantum
Mechanicsl
probability
distribution
of
the
electron wave function of
2D state confined by
“corrals”
made
of
adsorbed atoms.
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Quantum Mechanics
Lecture 37 Slide 53
Corralling electrons…
Introduction
Section 0
Lecture 1
Slide 54
STM used to make direct
maps of the Quantum
Mechanicsl
probability
distribution
of
the
electron wave function of
2D state confined by
“corrals”
made
of
adsorbed atoms.
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Quantum Mechanics
Lecture 37 Slide 54
Corralling electrons…
Introduction
Section 0
Lecture 1
Slide 55
STM used to make direct
maps of the Quantum
Mechanicsl
probability
distribution
of
the
electron wave function of
2D state confined by
“corrals”
made
of
adsorbed atoms.
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Quantum Mechanics
Lecture 37 Slide 55
Applications of knowledge on the atomic scale…
Feynman: “Plenty of
room at the bottom”
– Inevitability of small
– Interface of
quantum mechanics
with applications
Introduction
Section 0
Lecture 1
Slide 56
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Quantum Mechanics
Lecture 37 Slide 56
Moving atoms one layer at a time…
Introduction
Section 0
Lecture 1
Slide 57
Molecular Beam
Epitaxy
INTRODUCTION TO Modern Physics PHYX 2710
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Physics of Technology—PHYS 1800
Spring 2009
Quantum Mechanics
Lecture 37 Slide 57
Moving atoms one at a time…
Introduction
Section 0
Lecture 1
Slide 58
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Quantum Mechanics
Lecture 37 Slide 58
Moving atoms one at a time…
Introduction
Section 0
Lecture 1
Slide 59
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Quantum Mechanics
Lecture 37 Slide 59
Engineering Nanomachines
Introduction
Section 0
Lecture 1
Slide 60
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Quantum Mechanics
Lecture 37 Slide 60
Designer Molecules
Introduction
Section 0
Lecture 1
Slide 61
INTRODUCTION TO Modern Physics PHYX 2710
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Spring 2009
Quantum Mechanics
Lecture 37 Slide 61
Moving many atoms
Shen’s wor
STM images of the H-terminated Si(100) surfaces
Electron stimulated
H/D-desorption
from Si(100)-2x1
surface
200Åx200Å
USU
Nanolithography
Lab Introduction
1x1
Dihydride
Si
H
Section 0
Lecture 1
2x1
Monohydride
3x1
Monohydride + Dihydride
Slide 62
TC Shen
INTRODUCTION TO Modern Physics PHYX 2710
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Spring 2009
Quantum Mechanics
Lecture 37 Slide 62
Here at USU, TC Shen can make wires 1 atom wide!
An atom is ~0.1 nm across.
The moon is 4x108 m from the Earth (see front cover).
How many atoms, in a 1 atom wide wire,
would it take to reach the Moon?
How much would this amount of Cu weigh?
Introduction
Section 0
Lecture 1
Slide 63
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
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Spring 2009
Quantum Mechanics
Lecture 37 Slide 63
Atomic scale electronics
Single electron transistor
Chips ot the quantum scale
Introduction
Section 0
Lecture 1
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Slide 64
Transistors on a chip that
switch with a single
electron
Quantum Mechanics
Lecture 37 Slide 64
Quantum Computing
Macro to Micro
Micro to Nano
Nano to Sub-nano
Introduction
Section 0
Lecture 1
Slide 65
INTRODUCTION TO Modern Physics PHYX 2710
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Spring 2009
Quantum Mechanics
Lecture 37 Slide 65
Watching stuff happen…
Introduction
Chemistry time scales
STM
Femtosecond probes
Section 0
Lecture 1
Slide 66
INTRODUCTION TO Modern Physics PHYX 2710
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Spring 2009
Quantum Mechanics
Lecture 37 Slide 66
Femtosecond spectroscopy at USU…
USU Femtosecond
Spectroscopy Lab
D. Mark Riffe
Introduction
Section 0
Lecture 1
Slide 67
Probing dynamics of
hot electrons
INTRODUCTION TO Modern Physics PHYX 2710
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Spring 2009
Quantum Mechanics
Lecture 37 Slide 67
What We Know About Atoms
Nucleus
protons+ neutrons
1-10 fermi (fm)
e
1 fm=10-15 m
Atomic number (Z)= number of protons
p, n
Atom
Atoms are electrically neutral
0.1 nm= 1Å
1 Å=10-10 m
Z= number of electrons
Chemical properties are determined by electron configurations.
Chemically active : single e (alkali) or vacancy (halogene) in the outer shell
Introduction
Section 0
Lecture 1
Slide 69
Chemically inert : completely filled outer shells
Ion : atom lost or gained one or more electrons
INTRODUCTION TO Modern Physics PHYX 2710
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Valence electrons : electrons in the outer shell
Physics of Technology—PHYS 1800
Spring 2009
Quantum Mechanics
Lecture 37 Slide 69
Structural Models of the Atom
Thomson “Plumb
Pudding” Model
Aristotle’s
“Point” Model
e
 200
r
Introduction
Ze
Section 0
Rutherford “Point
Nucleus” Model
Lecture 1
2
r  2a0
Slide 70
INTRODUCTION TO Modern Physics PHYX 2710
Bohr “Planetary” Model
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
QM “Probability” Model
Quantum Mechanics
Lecture 37 Slide 70
The Uncertainty Principle
It can be shown that the minimum of the product of the
two conjugate observables is  2
xp   2
and
Et   2
Usually the uncertainty product is much greater than  2
If an excited energy of an atom has a lifetime τ, its
energy cannot be known better than  2
Accuracy of the position measurements depends on
wavelength.
Smaller wavelength means more momentum.
No observation will not disturb the subject.
Introduction
Section 0
Lecture 1
Slide 71
If a particle is confined in a space of length L, p   2 L Werner Heisenberg
Uncertainty Principle 1927
The kinetic energy of the particle must be greater
2
2
Nobel Prize 1932
than a minimum, p  
Zero-point
energy
2
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
2m
8mL
Physics of Technology—PHYS 1800
Spring 2009
Quantum Mechanics
Lecture 37 Slide 71
The Uncertainty Principle
Changes in momentum Uncertainty in position
Introduction Section 0 Lecture 1 Slide 72
determined by photon
imparted by photon:

probe wavelength:
p  h 
INTRODUCTION TO Modern Physics PHYX 2710
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Physics of Technology—PHYS 1800
Spring 2009
p x  h  
x  
Quantum Mechanics
Lecture 37 Slide 72
Atomic Spectra
Introduction
Section 0
Lecture 1
Slide 73
Atomic Emission Spectrophotometer
INTRODUCTION TO Modern Physics PHYX 2710
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Spring 2009
Atomic Emission Spectrum
of Hydrogen
Quantum Mechanics
Lecture 37 Slide 73
The First Excited States Wave Functions of H-atom
1st excited state has three degenerated states
 200
32
n=2, l=0, m=0

Zr   Zr 2 a0

 200  C200  2   e
a0 

n=2, l=1, m=0
 210  C210
n=2, l=1, m=±1  211  C211
 210
Zr  Zr 2 a0
e
cos 
a0
Zr  Zr 2 a0
e
sin e i
a0
 211
2
Introduction
Section 0
r  2a0
2
pr 
2
Lecture 1
 210 r 2
2
 200 r 2
2
Slide 74
2
INTRODUCTION TO Modern Physics PHYX 2710
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Physics of Technology—PHYS 1800
Spring 2009
Bohr model:
Quantum Mechanics
r a0
6
4
r  n2
a0
Z
Lecture 37 Slide 74
Probability Distributions for Hydrogen Atom
Introduction
Section 0
Lecture 1
Slide 75
INTRODUCTION TO Modern Physics PHYX 2710
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Spring 2009
Quantum Mechanics
Lecture 37 Slide 75
Periodic Table
Introduction
Section 0
Lecture 1
Slide 76
INTRODUCTION TO Modern Physics PHYX 2710
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Physics of Technology—PHYS 1800
Spring 2009
Quantum Mechanics
Lecture 37 Slide 76
Formation of Bands in Solids
Introduction
Section 0
Lecture 1
Slide 77
INTRODUCTION TO Modern Physics PHYX 2710
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Spring 2009
Quantum Mechanics
Lecture 37 Slide 77
An integrated circuit consists of several transistors, diodes,
resistors, and electrical connections all built into a single
tiny chip of semiconductor material, usually silicon.
– This allows the production of circuits much smaller than circuits
made from individual transistors or vacuum tubes.
– A computer that would fill a large room can now be reduced to the
size of a hand-held calculator.
The starting point
in producing
integrated circuits
is a polished
wafer of singlecrystal silicon.
Several identical
Introduction Section 0
circuits are usually
imprinted on a
single silicon
wafer.
Lecture 1
Slide 78
INTRODUCTION TO Modern Physics PHYX 2710
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Spring 2009
Quantum Mechanics
Lecture 37 Slide 78
– The wafer is cut into individual chips, each containing a miniature circuit.
– The final steps involve making electrical connections to the chip, packaging the
chip in a sealed plastic enclosure, and testing the resulting circuit.
Introduction
Section 0
Lecture 1
Slide 79
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Quantum Mechanics
Lecture 37 Slide 79
– Rows of packaged microchips are used on a single circuit board of a computer.
– Competition to produce ever smaller and faster circuitry continues to push the
technology forward.
Research in the
condensed-matter
physics of
semiconducting
elements and
compounds has
become one of the
most active areas in
modern physics.
Introduction Section 0
The revolution
in
electronics technology
is still proceeding.
Lecture 1
Slide 80
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
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Spring 2009
Quantum Mechanics
Lecture 37 Slide 80
Superconductors and Other New Materials
Superconductivity is a phenomenon in which
the resistance to the flow of electric current
completely disappears.
The resistance of many
metals drops abruptly to
zero at the critical
temperature Tc.
Introduction
Section 0 once
Lecture 1
An electric
current,
started, would flow
indefinitely with no source
of power.
Slide 81
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Quantum Mechanics
Lecture 37 Slide 81
The Meissner Effect
One striking property of a superconductor is
that it will completely exclude magnetic field
lines produced by an external magnet or
electrical current.
A magnet brought near a
superconducting material will
be repelled.
Section
0 Lecture
1 Slide 82
A smallIntroduction
magnet
can
levitate
above a superconducting disk
cooled with liquid nitrogen.
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Quantum Mechanics
Lecture 37 Slide 82
Physics of Technology
Next Recitation:
Math and Problem Solving Review
Tuesday 1:30-2:45
ESLC 53
Review Appendices A,B,C
Next Class:
Introduction
Section 0
Lecture 1
Wed
Slide 83 10:30-11:20
BUS 318 room.
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Quantum Mechanics
Lecture 37 Slide 83
Inconsistencies in Physics cira 2009
Statistical Mechanics
• Fermions,
Bosons and Anyons
•Bose-Einstein Condensates
•Superconductivity
•Stellar Evolution
• SM of Black Holes
• Time and Entropy
Conservation Laws
•
•
•
Electricity & Magnetism •
Maxwell Equations (c1880)
Energy
Linear & Angular Momentum
Charge, Spin
Lepton and Baryon Number
Heavy Fermions and HTSC
Chaotic and complex systems
Gravity………………
•
•
•
•
•
General Relativity
Space and time
Inconsistent with QM
Search for dark matter
Fixed gravitational constant?
Weak Nuclear Force
• Radioactivity
• CPT violations?
GUT’s and TOE’s
Quantum Mechanics
Section 0 Lecture 1 Slide 84
• Existence ofIntroduction
atoms
Strong Nuclear Force
•Schrodinger/Dirac Equation
•Composition of subatomic particles
• Sub-atomic particles
•Matter/anitmatter imbalance
• Probabilistic approach
•Decay ratios and particle masses
•Teleportation INTRODUCTION TO Modern Physics PHYX 2710
•Search for Higgs Bosons
Fall 2004
•Entwined states
•Nature of strong hadron force
•Sub-Planck length physics
•Proton decay
Physics of Technology—PHYS 1800
Spring 2009
Quantum Mechanics
• Combining Standard model
and Gravity
• String Theory
Lecture 37 Slide 84
The forces in the universe have also been grouped
into a few fundamental forces:
– The primary force responsible for binding the quarks in
neutrons, protons, and other baryons and mesons is
the strong nuclear interaction.
– The weak nuclear force is involved in the interactions
of leptons, such as beta decay.
– The electric force and magnetic force have been
combined into the electromagnetic force.
Introduction
Section 0
Lecture 1
Slide 85
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Quantum Mechanics
Lecture 37 Slide 85
– The standard model has now unified the
electromagnetic force with the weak nuclear force to
form the electroweak force.
– A Grand unified theory (GUT) which will unify the
strong force with the electroweak force is much sought
after.
– This leaves only the gravitational force.
– A Theory of everything (TOE) may someday unify all
forces, including gravity.
Introduction
Section 0
Lecture 1
Slide 86
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Quantum Mechanics
Lecture 37 Slide 86
Have you ever seen an atom?
Why do we think
atoms exist?
Introduction
Section 0
Do you believe
in atoms?
Lecture 1
Slide 87
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Quantum Mechanics
Lecture 37 Slide 87
Radioactivity and the Discovery of the
When Becquerel placed aNucleus
piece of phosphorescent material
on a covered photographic plate, the developed plate
showed a silhouette of the sample.
Radiation apparently was passing from these materials to
expose the film.
Introduction
Section 0
Lecture 1
Slide 88
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
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Spring 2009
Quantum Mechanics
Lecture 37 Slide 88
The basic building blocks of the nucleus are the proton
and the neutron.
– Their masses are nearly equal.
– The proton has a charge of +1e while the neutron is
electrically neutral.
This explains both the charge and the mass of the
nucleus.
– An alpha particle with charge +2e and mass 4 x mass of the
proton is composed of two protons and two neutrons.
– A nitrogen nucleus with a mass 14 times the mass of a
hydrogen nucleus and a charge 7 times that of hydrogen is
composed of seven protons and seven neutrons.
Introduction
Section 0
Lecture 1
Slide 89
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Quantum Mechanics
Lecture 37 Slide 89
Introduction
Section 0
Lecture 1
Slide 90
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Quantum Mechanics
Lecture 37 Slide 90
Radioactive Decay
Becquerel discovered natural radioactivity in 1896.
By 1910, Rutherford and others demonstrated that
one element was actually being changed into
another during radioactive decay.
The nucleus of the atom itself is modified when a
decay occurs.
– For example, Marie and Pierre Curie isolated the highly
radioactive element radium which emitted primarily
alpha particles.
Introduction
Section 0
Lecture 1
Slide 91
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
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Spring 2009
Quantum Mechanics
Lecture 37 Slide 91
Nuclear Reactions and Nuclear Fission
In addition to spontaneous radioactive decays,
changes in the nucleus may be produced
experimentally through nuclear reactions.
Introduction
Section 0
Lecture 1
Slide 95
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
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Spring 2009
Quantum Mechanics
Lecture 37 Slide 95
Nuclear Reactors
Fermi’s strategy to achieve a chain reaction with
natural or slightly enriched uranium:
– Slow the neutrons down between fission reactions using a
material called a moderator.
– Control rods are used to absorb the neutrons to slow the
reaction as desired.
Fermi’s “pile” was the first
human-produced nuclear
reactor.
Introduction
Section 0asLecture
Graphite blocks
served
the moderator.
Control rods were cadmium,
but today’s reactors use
boron.
1
Slide 96
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Quantum Mechanics
Lecture 37 Slide 96
Modern Power Reactors
Most reactors today use ordinary (light) water as the moderator.
This requires enrichment of the fuel to 3% U-235.
The advantage is that the water can also be used as a coolant.
Introduction
Section 0
Lecture 1
Slide 97
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Quantum Mechanics
Lecture 37 Slide 97
A hydrogen bomb involves nuclear fusion rather than
fission.
– Nuclear fusion is another kind of nuclear reaction that also
releases large quantities of energy.
– Fusion is the energy source of the sun and other stars as well as
of thermonuclear bombs.
– In a sense, it is the opposite of fission: very small nuclei such as
hydrogen, helium, and lithium combine to form larger nuclei.
– As long as the mass of the reaction products is less than the mass
of the original isotopes, energy is released.
One
possible reaction is the
combination of two isotopes
of hydrogen, deuterium and
tritium, toIntroduction
form helium-4
plus
Section 0 Lecture
a neutron:
1
Slide 101
INTRODUCTION TO Modern Physics PHYX 2710
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Spring 2009
Quantum Mechanics
Lecture 37 Slide 101
Can we generate power from controlled fusion?
Producing fusion reactions for a commercial power source
has not yet been accomplished.
– Confining the fuel at very high temperatures in a very small space
presents extreme difficulties.
Experimental
reactors such
as the Tokamak Fusion Test
Reactor at Princeton, NJ,
have generated energy from
fusion, but they have not
reached the break-even
point, where as much energy
Section 0 to
Lecture
is releasedIntroduction
as is required
initiate the reaction.
Research on this problem
may someday reach that
goal.
1
Slide 103
INTRODUCTION TO Modern Physics PHYX 2710
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Spring 2009
Quantum Mechanics
Lecture 37 Slide 103
Quarks and Other Elementary Particles
Atoms were once thought to be the basic building blocks of all
matter.
We now know atoms consist of electrons, protons, and
neutrons.
Neutrons and protons also have a substructure of quarks.
Introduction
Section 0
Lecture 1
Slide 104
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
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Spring 2009
Quantum Mechanics
Lecture 37 Slide 104
Where will this all end?
What are quarks and why do we believe they exist?
Will we someday discover that quarks also have a
substructure?
Recent advances in high-energy physics have produced the
standard model.
Particle
accelerators like CERN
in Europe and Fermilab in the
U.S. are used to bombard targets
with fast-moving particles.
Particle detectors are used to
study what
emerges from these
Introduction Section 0 Lecture 1
collisions.
For example, particle tracks in a
bubble chamber provide
information on the new particles
produced in collisions or decays.
Slide 105
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
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Spring 2009
Quantum Mechanics
Lecture 37 Slide 105
... to the largest.
How was
the
universe
formed?
How is it
changing?
Introduction
Section 0
Lecture 1
Slide 106
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
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Spring 2009
Quantum Mechanics
Lecture 37 Slide 106
The Michelson-Morley Experiment
Michelson and Morley used an interferometer to detect
small differences in the velocity of light or in the
distance that the light traveled.
Light waves traveling
along the two
perpendicular arms
interfere to form a
Introduction Section 0 Lecture 1
pattern
of light and
dark fringes.
Slide 107
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
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Spring 2009
Quantum Mechanics
Lecture 37 Slide 107
The Michelson-Morley Experiment
At some time during the year the earth should be
moving relative to the ether.
No fringe shift was observed; the experiment failed to
detect any motion of the earth relative to the ether.
This “failure” was a
very important
Introduction Section 0result!
Lecture 1
Slide 108
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Quantum Mechanics
Lecture 37 Slide 108
Einstein’s Postulates of
Special Relativity
Einstein’s solution to the dilemma of the ether and the
speed of light was both simple and radical.
– Postulate 1: The laws of physics are the same in any
inertial frame of reference.
– Postulate 2: The speed of light in a vacuum is the
same in any inertial frame of reference, regardless of
the relative motion of the source and observer.
The firstIntroduction
is just
a reaffirmation of the principle of
Section 0 Lecture 1 Slide 109
relativity stated earlier.
The second is much more radical: light does not
behave like most waves or moving objects.
INTRODUCTION TO Modern Physics PHYX 2710
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Spring 2009
Quantum Mechanics
Lecture 37 Slide 109
Newton’s Laws and
Mass-Energy Equivalence
Accepting Einstein’s postulates requires some
major changes in how we think about space
and time.
For example, does Newton’s second law of
motion still apply when objects are moving at
large velocities?
F = ma = p / t
Introduction Section 0 Lecture 1 Slide 110
In order to maintain conservation of momentum,
Einstein redefined momentum as
p = mv
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Quantum Mechanics
Lecture 37 Slide 110
General Relativity
What happens if our frame of reference is
accelerating?
Imagine that we are in a
moving elevator, for example.
If the elevator is moving with constant
velocity, no experiment that we can do
inside the elevator could establish
whether or
not we
are
moving.
Introduction
Section
0 Lecture
1 Slide 111
If the elevator is accelerating, a
bathroom scale would register a
greater weight.
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Quantum Mechanics
Lecture 37 Slide 111
Similarly, space is curved near a very strong
gravitational field.
– This represents how things might be pulled into
the center of the field.
– Since light rays are bent by strong gravitational
fields, they can be pulled into the center of the
field as well as particles having some mass.
Introduction
Section 0
Lecture 1
Slide 112
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Quantum Mechanics
Lecture 37 Slide 112
This figure is a two-dimensional representation
of a black hole.
– Black holes are thought to be very massive
collapsed stars, which generate an extremely
strong gravitational field.
– Space is very curved in their vicinity.
Introduction
Section 0
Lecture 1
Slide 113
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Quantum Mechanics
Lecture 37 Slide 113
Einstein’s theories of special and general relativity have had an enormous impact
on our concepts of space and time.
Special relativity deals with reference frames that, although
moving at speeds near the speed of light, are still inertial (nonaccelerating).
General relativity deals with accelerated reference frames.
The predictions of these theories have been well confirmed.
– For example, the energy released in nuclear reactions is a result of
mass-energy equivalence.
Section 0 Lecture 1 Slide 114
– Also, Introduction
astronomical
observations of the bending of starlight is evidence of
the principle of equivalence between gravity and acceleration.
These ideas excite the imagination and are still very active areas
of research.
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Quantum Mechanics
Lecture 37 Slide 114
Cosmology and the Beginning of Time
We have now looked into the extremely small:
– Quarks make up protons and neutrons, which form the nucleus.
– Atoms consist of the nucleus and the surrounding electrons.
– Atoms make up molecules and the ordinary matter of our world.
What about the very large?
– The earth is part of the solar system which includes the sun.
– The sun is just one star in our galaxy, which is just one galaxy in
our Local Group of galaxies.
– These groups of galaxies make up larger groups, and ultimately,
the universe.
What can our knowledge of atoms, nuclei, and quarks tell us
about the universe?
Introduction
Section 0
Lecture 1
Slide 115
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Quantum Mechanics
Lecture 37 Slide 115
Hurtzsprung-Russell (H-R) Diagram
100R
1000R
Betelgeuse
Polaris
1R
Antares
Arcturus
Sirius A
0.01R
Sun
Sirius B
Introduction
Section 0
Lecture 1
Slide 116
LM4
 Physics
M PHYX 2710
INTRODUCTION T
TOeModern
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Quantum Mechanics
Lecture 37 Slide 116