1 Blackbody Radiation Photoelectric Effect Wave-Particle Duality SPH4U Everything comes unglued The predictions of ―classical physics‖ (Newton‘s laws and Maxwell‘s equations) are sometimes completely, utterly WRONG. classical physics says that an atom‘s electrons should fall into the nucleus and STAY THERE. No chemistry, no biology can happen. classical physics says that toaster coils radiate an infinite amount of energy: radio waves, visible light, X-rays, gamma rays,… The source of the problem It‘s not possible, even ―in theory‖ to know everything about a physical system. knowing the approximate position of a particle corrupts our ability to know its precise velocity (―Heisenberg uncertainty principle‖) Particles exhibit wave-like properties. interference effects! The scale of the problem Let‘s say we know an object‘s position to an accuracy Dx. How much does this mess up our ability to know its speed? Here‘s the connection between Dx and Dv (Dp = mDv): That‘s the ―Heisenberg uncertainty principle.‖ h 6.610 -34 J·s 4 h px DD ―It is physically impossible to predict simultaneously the exact position and exact momentum of a particle.‖
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1
Blackbody Radiation
Photoelectric Effect
Wave-Particle Duality
SPH4U
Everything comes unglued
The predictions of ―classical physics‖ (Newton‘s
laws and Maxwell‘s equations) are sometimes
completely, utterly WRONG. classical physics says that an atom‘s electrons should fall
into the nucleus and STAY THERE. No chemistry, no
biology can happen.
classical physics says that toaster coils radiate an infinite
amount of energy: radio waves, visible light, X-rays,
gamma rays,…
The source of the problem
It‘s not possible, even ―in theory‖ to know
everything about a physical system. knowing the approximate position of a particle corrupts
our ability to know its precise velocity (―Heisenberg
Let‘s say we know an object‘s position to an accuracy Dx.
How much does this mess up our ability to know its speed?
Here‘s the connection between Dx and Dv (Dp = mDv):
That‘s the ―Heisenberg uncertainty principle.‖ h 6.610-34 J·s
4
hp x
D D
―It is physically impossible to predict simultaneously the exact
position and exact momentum of a particle.‖
2
Atomic scale effects
Small Dx means large Dv since4
hv
m xD
D
Example: an electron (m = 9.110-31 kg) in an atom is confined to a region of size x ~ 510-11 m.
How is the minimum uncertainty in its velocity?
Plug in, using h = 6.610-34 to find v > 1.1106 m/sec
Example
The speed of an electron (m = 9.110-31 kg) is measured to
have a value of 5 x 103 m/s to an accuracy of 0.003 percent.
Determine the uncertainty in determining its position.
31 3
27
9.11 10 5.00 10
4.56 10
mkg
s
kg m
s
p mv
27
31
0.00003 4.56
0.
10
1.37 10
00003
kg m
s
kg
p
m
p
s
D
34
31
4
6.63 10
44 1.37 1
0.38
0
3 8 10
5
4
. 5
J shx
kg mp
s
m
m
hx p
m
D
D
D D
Example
The speed of an bullet (m = 0.020 kg) is measured to have a
value of 300 m/s to an accuracy of 0.003 percent. Determine
the uncertainty in determining its position.
0.020 300
6
m
p
kgs
m
k
v
g m
s
4
0.00003 6
1.8 1
0.
0
00003
k
p
m
s
k
p
g
g m
s
D
3
34
4
1
6.63 10
44 1.8
2.93 1
10
0
4
m
J shx
h
m
x p
kgp
s
D
D
D D
Example
A proton has a mass of 1.67 x 10-27 kg and is close to
motionless as possible. What minimum uncertainty in its
momentum and in its kinetic energy must it have if it is
confined to a region :
(a) 1.0 mm
(b) An atom length 5.0 x 10-10m
(c) About the nucleus of length 5.0 x 10-15m
3
ExampleA proton has a mass of 1.67 x 10-27 kg and is close to
motionless as possible. What minimum uncertainty in its
momentum and in its kinetic energy must it have if it is
confined to a region :
(a) 1.0 mm
3
34
3
2
6.63 10
4 4 1.0 10
4
5.28 10
J
h
shp
x
x p
m
kg m
s
D
D
D
D
34
5
27 3
6.63 10
4 4 1.67 10 1.0 10
3.16 10
p m
J sh
m
s
v
vm x kg m
D
D
D
D
2
2
2
3
7 5
7
11.67 10 3.16
8.33 1
1
0
02
2
1m
kgs
J
KE mv
ExampleA proton has a mass of 1.67 x 10-27 kg and is close to
motionless as possible. What minimum uncertainty in its
momentum and in its kinetic energy must it have if it is
confined to a region :
(b) An atom length 5.0 x 10-10m
3
25
4
10
6.63 10
4 4 5.0 10
1.0 0
4
6 1
J shp
kg
x
s
x
m
m
hp
D
D D
D
34
27 10
6.63 10
4 4 1.67 10 5.0 1
2
0
63.
J shv
m
p m
x m
v
m
s
kg
D
D
D
D
2
2
27
24
11.67 10 63
3.33 1
22
1
2
0
.m
kgs
m
J
KE v
ExampleA proton has a mass of 1.67 x 10-27 kg and is close to
motionless as possible. What minimum uncertainty in its
momentum and in its kinetic energy must it have if it is
confined to a region :
(c) About the nucleus of length 5.0 x 10-15m
3
20
4
15
6.63 10
4 4 5.0 10
1.0 0
4
6 1
J shp
kg
x
s
x
m
m
hp
D
D D
D
34
6
27 20
6.63 10
4 4 1.
6.32 10
67 10 1.06 10
J shv
m x kg m
p
m
s
m v
D
D
D D
2
2
2
1
7 6
4
11.67 10 6.32
3.33 10
0
2
2
1
1m
kgs
K
J
mv
m
E
Notice that when we consider a particle
(say a proton), that is confined to a small
region, the Quantum Mechanics requires
that such a particle cannot have a precise
momentum (or even momentum of zero).
This means that even at absolute zero, this
proton must have kinetic energy. This
energy is called the ―zero point energy‖,
and there is no way to avoid this.
Quantum Mechanics!
At very small sizes the world is VERY
different!
Energy can come in discrete packets
Everything is probability; very little is absolutely
certain.
Particles can seem to be in two places at same
time.
Looking at something changes how it behaves.
4
Another Consequence of
Heisenberg‘s Uncertainty
Principle
A quantum particle can never be in a state of rest,
as this would mean we know both its position and
momentum precisely
Thus, the carriage will
be jiggling around the
bottom of the valley
forever
Blackbody Motivation
• The black body is importance in thermal radiation theory and practice.
• The ideal black body notion is importance in studying thermal radiation and electromagnetic radiation transfer in all wavelength bands.
• The black body is used as a standard with which the absorption of real bodies is compared.
Hot objects glow (toaster coils, light bulbs, the sun).
As the temperature increases the color shifts from Red to
Blue.
The classical physics prediction was completely wrong! (It
said that an infinite amount of energy should be radiated by
an object at finite temperature.)
Blackbody RadiationDefinition of a black body
A black body is an ideal body which allows
the whole of the incident radiation to pass
into itself ( without reflecting the energy ) and
absorbs within itself this whole incident
radiation. This propety is valid for radiation
corresponding to all wavelengths and to all
angels of incidence. Therefore, the black
body is an ideal absorber and emitter of
radaition. The blackbody will then radiate at
a wavelength that is related to its absolute
temperature. One should picture a hot oven
with an open door emitting radiation into its
cooler surroundings or, if the surroundings
are hotter, one pictures a cool oven with an
open door taking in radiation from its
surroundings. It is the open oven door, which
is meant to look black—and hence absorbs
all colours or frequencies—that gives rise to
the term black body.
5
Maxwell‘s Classical Theory
Rayleigh-Jeans Law
The Ultraviolet Catastrophe
4
2),(
ckTTI
This formula also had a
problem. The problem was
the term in the denominator.
For large wavelengths it fitted
the experimental data but it
had major problems at
shorter wavelengths.
Planck Law
Higher temperature: peak intensity at shorter
22 1( , )
5
1
hcI T
hc
kTe
Blackbody Radiation:
First evidence for Q.M.
Max Planck found he could explain these curves if he
assumed that electromagnetic energy was radiated in discrete
chunks, rather than continuously.
The ―quanta‖ of electromagnetic energy is called the photon.
Energy carried by a single photon is
E = hf = hc/
Planck‘s constant: h = 6.626 X 10-34 Joule sec
E = nhf, n=1, 2, 3, 4
6
Blackbody Radiation:
First evidence for Q.M.
It was more difficult for atoms to absorb very high energy
photons (short wave lengths thus high frequency).
E = nhf, n=1, 2, 3, 4
Planck himself matched mathematics to the data. He
used mathematics as a device to obtain the correct
answer which he initially believed was still in classical
Newtonian physics.
QuestionsA series of light bulbs are glowing red, yellow, and blue.
Which bulb emits photons with the most energy?
The least energy?
Which is hotter?
(1) stove burner glowing red
(2) stove burner glowing orange
Blue! Lowest wavelength is highest energy.
E = hf = hc/
Red! Highest wavelength is lowest energy.
Hotter stove emits higher-energy photons
(shorter wavelength = orange)
Colored Light
Which coloured bulb‘s filament is hottest?
1) Red
2) Green
3) Blue
4) Same
Coloured bulbs are identical on the inside – the glass is tinted
to absorb all of the light, except the color you see.
max
Visible Light
Photon
A red and green laser are each rated at
2.5mW. Which one produces more
photons/second?
1) Red 2) Green 3) Same
Red light has less energy/photon so if they both have
the same total energy, red has to have more photons!
# photons Energy/second
second Energy/photon
Power
Energy/photon
Power
hf
7
Wein‗s Law
Wein Displacement Law
- It tells us as we heat an object up, its
color changes from red to orange to
white hot.
- You can use this to calculate the
temperature of stars.
The surface temperature of the Sun is
5778 K, this temperature
corresponds to a peak emission =
502 nm = about 5000 Å.
T
bmax
Wien‘s Displacement Law
(nice to know)
To calculate the peak wavelength
produced at any particular temperature,
use Wien‘s Displacement Law:
T · peak = 0.2898*10-2 m·K
temperature in Kelvin!
The Wave – Particle Duality
OR
Light Waves
Until about 1900, the classical wave theory of light described
most observed phenomenon.
Light waves:
Characterized by:
Amplitude (A)
Frequency (n)
Wavelength ()
Energy of wave is a A2
8
Waves or Particles ?
Ball, Car, cow, or point like objects called particles.
They can be located at a location at a given time.
They can be at rest, moving or accelerating.
Falling Ball
Ground level
Physical Objects:
Waves or Particles ?
Ripples, surf, ocean waves, sound waves, radio waves.
Need to see crests and troughs to define them.
Waves are oscillations in space and time.
Direction of travel, velocity
Up-down
oscillations
Wavelength ,frequency, velocity and amplitude defines waves
Common types of waves:
Particles and Waves: Basic difference in behaviour
When particles collide they cannot pass through each other !
They can bounce or they can shatter
Waves and Particles Basic difference:
Waves can pass through each other !
As they pass through each other they can enhance or cancel
each other
Later they regain their original form !
9
And then there was a
problem…
In the early 20th century, several effects were observed
which could not be understood using the wave theory of
light.
Two of the more influential observations were:
1) The Photo-Electric Effect
2) The Compton Effect
Photoelectric Effect
Electrons are attracted to the (positively charged) nucleus by the
electrical force
In metals, the outermost electrons are not tightly bound, and can
be easily ―liberated‖ from the shackles of its atom.
It just takes sufficient energy…
Classically, we increase the energy
of an EM wave by increasing the
intensity (e.g. brightness)
Energy a A2
But this doesn‘t work ??
PhotoElectric Effect
An alternate view is that light is acting like a particle
The light particle must have sufficient energy to ―free‖ the
electron from the atom.
Increasing the Intensity is simply increasing the number
of light particles, but its NOT increasing the energy of each
one!
Increasing the Intensity does diddly-squat!
However, if the energy of these ―light particle‖ is related to their
frequency, this would explain why higher frequency light can
knock the electrons out of their atoms, but low frequency light
cannot…
Nobel Trivia
For which work did Einstein receive the Nobel Prize?
1) Special Relativity E = mc2
2) General Relativity Gravity bends Light
3) Photoelectric Effect Photons
4) Einstein didn‘t receive a Nobel prize.
10
Photoelectric Effect
Light shining on a metal can ―knock‖
electrons out of atoms.
Light must provide energy to overcome
Coulomb attraction of electron to nucleus
The Apparatus
When the emission of photoelectrons from the cathode occurs, they travel across the vacuum tube toward the anode, due to the applied potential. Even when the variable potential is dropped to zero, the current does not drop to zero, because the kinetic energy of the electrons is still adequate enough to allow some to cross the gas (thus creating a current).
If we make the variable source of electrical potential negative then this has the effect of reducing the electron flow. If the anode is made more negative, relative to the cathode, a potential difference, the cutoff potential, V0, is reached when the electrons are all turned back.
The cutoff potential corresponds to the maximum kinetic energy of the photoelectrons. They do not have the KE to make it across the gap.
Classical physics prediction
Electrons can be emitted regardless of the incident frequency, though it
will take longer time for smaller incident wave amplitude.
There should be a time delay between the wave illumination and the
emission of electrons.
The higher the wave intensity, the higher electron energy, and thus the
higher the stopping voltage.
1
f
Modern physics explanation
The electromagnetic wave consists of many lumped energy particles
called photons.
The energy of each individual photon is given by the Joule
Problem: According to the wave picture of light, the incident X-ray gives up
energy to the electron, and emerges with a lower energy (ie., the amplitude
is lower), but must have 21.
M
A
T
T
E
R
Incident X-ray
wavelength
12 > 1
Scattered X-ray
wavelength
2
e
Electron comes flying out
Louis de Broglie
Quantum Picture to the RescueIf we treat the X-ray as a particle with zero mass, and momentum p = E / c,
everything works !
Incident X-ray
p1 = h / 1
e
Electron
initially at
rest
2 > 1
Scattered X-ray
p2 = h / 2
e
pe
e
Compton found that if the photon was treated like a particle with
mometum p=E/c, he could fully account for the energy & momentum
(direction also) of the scattered electron and photon! Just as if 2 billiard
balls colliding!
Compton Scattering (nice to know)
Compton assumed the
photons acted like other
particles in collisions
Energy and momentum were
conserved
The shift in wavelength is
(1 cos )o
e
h
m c D
Compton wavelength
21
DeBroglie‘s Relation
The smaller the wavelength the larger the photon‘s momentum!
The energy of a photon is simply related to the momentum by:
E = pc (or, p = E / c )
The wavelength is related to the momentum by: = h/p
The photon has momentum, and its momentum is given by simply p = h /
.
p = h /
Quantum Summary
Particles act as waves and waves act as
particles
Physics is NOT deterministic
Observations affect the experiment
Four QuantumParadoxes
Paradox 1 (non-locality):Einstein’s Bubble
Situation: A photon is emitted from an isotropic source.
22
Paradox 1 (non-locality):Einstein’s Bubble
Situation: A photon is emitted from an isotropic source.
Its spherical wave function Y expands like an inflating
bubble.
Paradox 1 (non-locality):Einstein’s Bubble
Question (Albert Einstein):
If a photon is detected at Detector A, how does the
photon’s wave function Y at the location of Detectors
B & C know that it should vanish?
Situation: A photon is emitted from an isotropic source.
Its spherical wave function Y expands like an inflating
bubble.
It is as if one throws a beer bottle into
Lake Ontario. It disappears, and its
quantum ripples spread all over the
Atlantic.
Then in Copenhagen, the beer bottle
suddenly jumps onto the dock, and the
ripples disappear everywhere else.
That’s what quantum mechanics says
happens to electrons and photons when
they move from place to place.
Paradox 1 (non-locality):Einstein’s Bubble
Experiment: A cat is placed in a sealed box containing a device that has a 50%
chance of killing the cat.
Question 1: What is the wave function of the cat just before the box is opened?
When does the wave function collapse?
Paradox 2 (Y collapse):Schrödinger’s Cat
1 1
2 2( dead + alive ?)Y
Question 2: If we observe Schrödinger, what is his wave function during the
experiment? When does it collapse?The question is, when
and how does the
wave function
collapse.
•What event collapses
it?
•How does the
collapse spread to
remote locations?
23
Paradox 3 (wave vs. particle):Wheeler’s Delayed Choice
A source emits one photon.
Its wave function passes
through slits 1 and 2, making
interference beyond the slits.
The observer can choose to either:
(a) measure the interference pattern at
plane s1, requiring that the photon travels
through both slits.
or
(b) measure at plane s2 which slit image it
appears in, indicating that
it has passed only through slit 2.
The observer waits until
after the photon has
passed the slits to decide
which measurement to
do.
*
**
Thus, the photon does not
decide if it is a particle or a
wave until after it passes
the slits, even though a particle
must pass through only one slit and a wave must pass
through both slits.
Apparently the measurement choice determines
whether the photon is a particle or a wave retroactively!
Paradox 3 (wave vs. particle):Wheeler’s Delayed Choice
Paradox 4 (non-locality):EPR ExperimentsMalus and Furry
An EPR (einstein Poldalsky Rosen)
Experiment measures the correlated
polarizations of a pair
of entangled photons, obeying
Malus’ Law [P(rel) = Cos2rel]
Paradox 4 (non-locality):EPR ExperimentsMalus and Furry
An EPR Experiment measures the
correlated polarizations of a pair
of entangled photons, obeying
Malus’ Law [P(rel) = Cos2rel]
The measurement gives the same result
as if both filters were in the same arm.
24
Paradox 4 (non-locality):EPR ExperimentsMalus and Furry
An EPR Experiment measures the
correlated polarizations of a pair
of entangled photons, obeying
Malus’ Law [P(rel) = Cos2rel]
The measurement gives the same result
as if both filters were in the same arm.
Furry proposed to place both photons in
the same random polarization state.
This gives a different and weaker
correlation.
Paradox 4 (non-locality):EPR ExperimentsMalus and Furry
Apparently, the measurement on the right side of the apparatus causes (in some sense of the word cause) the photon on the left side to be in the same quantum mechanical state, and this does not happen until well after they have left the source.
This EPR “influence across space time” works even if the measurements are light years apart.
Could that be used for FTL signaling? Sorry, SF fans, the answer is No!
FourInterpretations
of Quantum Mechanics
Scientists who subscribe to the Collapse interpretation make a
choice. They believe that when you accept the electron‘s wave
nature, you must give up on the electron‘s particle nature.
In this interpretation, the electron leaves the source as a particle that
is governed by one set of laws, but then ―expands‖ into a spread-out
wave as it passes through the slits. The electron is now governed by
new laws. However, before we can measure this wavy, spread-out
quantum electron it ―collapses‖ back into a particle and arrives at
only one of the many possible places on the screen.
The consequence of choosing the Collapse interpretation line of
thinking is that you must accept that an electron physically changes
from particle to wave and back again. These two realities, including
the laws that describe them, alternate uncontrollably
The Collapse Interpretation
25
The Pilot Wave interpretation avoids this unexplained collapse altogether. Scientists
who subscribe to this interpretation choose to believe that the electron always exists
as a classical particle and is only ever governed by one kind of physical law, for both
the familiar classical as well as quantum phenomena. However, to account for the
electron‘s wave behaviour this description requires the introduction of an invisible
guiding wave.
In this interpretation, wave-particle duality is explained by assuming that electrons
are real particles all of the time, and are guided by an invisible wave. The electron‘s
wave nature is attributed to this abstract wave, called a Pilot Wave, which tells the
electron how to move. To obtain the interference pattern in the double-slit experiment,
this wave must be everywhere and know about everything in the universe, including
what conditions will exist in the future. For example, it knows if one or two slits are
open, or if a detector is hiding behind the slits.
The Pilot Wave interpretation embodies all of the quantum behaviour, including all the
interactions between classical objects like the electron, the two-slit barrier, and the
measuring devices. In contrast to the Collapse interpretation where the collapsing
electron wave was considered real, in the Pilot Wave interpretation the wave is an
abstract mathematical tool. This interpretation has a consequence. The Pilot Wave
interpretation, which was invented to deal with an electron as a real physical object,
suffers the fate of being permanently beyond detection
The Pilot Wave InterpretationThe Many-Worlds Interpretation
Supporters of the Many Worlds interpretation, similar to the Pilot Wave idea,
choose to accept that electrons are classical particles. Then they go even further,
demanding that all elements of the theory must correspond to real objects—unlike
the collapsing electron or the Pilot Wave. Supporters insist on only measurable,
physical objects within the world. This world is constantly splitting into many
copies of itself.
When electrons demonstrate wave behaviour they exist in a superposition of many
different states. To Many Worlds supporters, who maintain the idea of an electron
as a classical particle, a parallel universe must exist for each of the electron‘s
possible states. When the electron reaches the slits, it has to choose which slit to
go through. At that moment, the entire universe splits into two. In one universe, the
electron passes through the left slit as a real particle. In the other universe it
passes through the right slit as a real particle. The consequence of accepting the
Many Worlds interpretation, with many quantum particles constantly facing similar
choices, is the requirement that our universe must be constantly splitting into an
almost infinite number of parallel universes, each having its own copy of every one
of us
The Copenhagen InterpretationAdvocates of the Copenhagen interpretation choose to limit their discussion directly to the
experiment and to the measurements on physical objects. Questions are restricted to what
can be seen and to what we actually do. They try to think about experiments in a very
honest way, without invoking extra theoretical ideas like the on-off switching of the Collapse
idea, or the guidance supplied by the invisible Pilot Wave, or the proposed splitting into
Many Worlds.
It is tempting to come up with mental pictures about what is happening that go beyond the
results of an experiment, and to try to interpret what is happening by means of those hidden
theoretical mechanisms. The previous interpretations attributed the mysterious wave–
particle duality to imaginative mathematics. In the Copenhagen interpretation much of this
mystery is attributed to what happens when an experimenter enters the lab and interacts
with the quantum mechanical system. With the Copenhagen perspective, the mathematics
only deals with the experimenter‘s information about measurement interactions with the
quantum mechanical system.
The consequence of accepting the Copenhagen interpretation is a fundamental restriction
on how much you can read into experimental results. We know that electrons are particles
when they are fired from the source, and we know that they are particles when they hit the
screen. What happens to electrons in the middle, what they are ―doing‖, or what they really
―are‖ is not possible to know. In the Copenhagen interpretation these are unfounded
questions. We may call an electron a wave or a particle, but ultimately those names are no