Transcript 2.5.3 Wave Particle Duality

5 Quantum Mechanics
G482 Electricity, Waves & Photons
2.5.1 Energy of
A Photon
2.5.2 The
Photoelectric
Effect
2.5.3 WaveParticle Duality
2.5.4 Energy
Levels in Atoms
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Index
Introduction....
The aim of this module is to introduce the concept of quantum behaviour. How do we know
that light is a wave?
The evidence for this comes from diffraction of light. However, this wave-like behaviour
cannot explain how light interacts with electrons in a metal.
A revolutionary model of light (photon model), developed by Max Planck and Albert
Einstein, is needed to describe the interaction of light with matter.
Physicists expect symmetry in nature. If light can have a dual nature, then surely particles
like the electron must also have a dual nature. We study the ideas developed by de Broglie.
The final section looks briefly at the idea that electrons in atoms have discrete bond
energies and they move between energy levels by either absorbing or by emitting photons.
There are many opportunities to discuss how theories and models develop with the history
of wave-particle duality.
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Practical Skills are assessed using OCR set tasks.
The practical work suggested below may be carried out as part of skill development.
Centres are not required to carry out all of these experiments.
This module does not lend itself to many experiments carried by the students. However, it
does contain many revolutionary ideas and engaging students in discussions is vital when
demonstrating some of the experiments.
Use a GM tube to ‘count’ gamma ray photons.
Determine the wavelength of light from different LEDs
Demonstrate the photoelectric effect using a photocell or a negatively charged zinc plate
connected to an electroscope.
Observe ‘diffraction rings’ for light passing through a tiny hole.
Demonstrate the diffraction of electrons by graphite.
Observe emission line spectra from different discharge tubes. (A hand-held optical
spectrometer can be used to observe Fraunhofer lines in daylight. Caution: Do not look
directly at the Sun.)
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Activities...
1. Discuss how wave and particle models of light
are both required in different contexts. Discuss
how de Broglie posed the question of whether
particles like electrons could also behave like
waves
2. Demonstrate electron diffraction in cathode ray
tube. Illustrate features of demonstration
including thin graphite layer
3. View narrow-slit or small hole interference of
light and/or see images of X-ray diffraction and
compare to electron diffraction patterns
h

4. Given the de Broglie equation calculate
mv
wavelength of wave associated with electron.
Use eV = ½ mv2 to give speed of electron in
cathode ray and calculate wavelength. Compare
to atomic spacing and discuss gap requirement
for diffraction. Give further examples of
wavelengths of particles from sub-atomic to
every-day
5. Discuss why duality and quantum phenomena
only apparent on very small scale
6. Summarise wave-particle duality with “travel as
a wave, interact as particles”
Resources....
1. Diffraction tube, E.H.T.
supply, darkened lab
2. Laser and small holes or
slits, darkened lab
3. Calculate speed required
for a person to have
wavelength similar to a
door. Calculate time taken
to travel 1 mm at this
speed and compare to, say,
age of universe
4. Explain double-slit results
with wave and particle
model, illustrate difficulty
of understanding elements
of quantum mechanics and
try to give “
interpretation” with waves
of probability
5. End of topic test
Points to Note…
1.
2.
3.
4.
5.
6.
Websites:
http://www.upscale.uto
ronto.ca/PVB/Harrison/
DoubleSlit/Flash/Histog
ram.html and
http://www.upscale.uto
ronto.ca/PVB/Harrison/
DoubleSlit/Flash/Doubl
eSlit.html
make good
illustrations of point
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2.5.3 Wave-Particle Duality (p178)
Assessable learning outcomes....
(a) explain electron diffraction as evidence for the wave nature of particles like
electrons;
(b) explain that electrons travelling through polycrystalline graphite will be
diffracted by the atoms and the spacing between the atoms;
(c) select and apply the de Broglie equation h/mv = 
(d) explain that the diffraction of electrons by matter can be used to determine
the arrangement of atoms and the size of nuclei.
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Discovery of the
Electron Video
3mins
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2.5.3 Wave-Particle Duality
2.5.3 Wave-Particle Duality
2.5.3 Wave-Particle Duality
Wave Particle Duality – p41
K
Should know that electron diffraction suggests the wave nature of particles and the
photoelectric effect suggests the particle nature of electromagnetic waves; details of
particular methods of particle diffraction are not expected.
Application of the de Broglie wavelength λ = h/mv formula where mv is the
momentum
S
Be able to complete calculations and sub into formulae. Also describe about
TEM/STM/Squids/MR
U
How particles can be thought of as having a wavelength.
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Concept Maps
By the end of this module of work you should understand how some of the elements
you have studied fit in with this map;
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Main Themes – coming together
Waves & Particle Duality
Photons
Photoelectric effect
E=hf = hc/ λ
Intensity of Light
Atomic Energy Levels
hf = E2 - E1
Line Spectra
Lasers
hf = Φ + KEmax
Particle behaviours
Wave behaviours
λ = h/mv = h/p
De Broglie Equation
Size of Atom
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Duality
The dual nature of light:
The diffraction of light provides evidence of light being wavelike in nature
The photo electric effect provides evidence of light being particle-like in nature
The dual nature of matter:
The diffraction of an electron beam directed at a thin metal film provides
evidence of matter being wavelike in nature ( also electron deflection in
electric and magnetic fields)
The rows of atoms in the metal crystals behave like light passing
through slits for it to happen should be  similar to size of atoms.
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Diffraction Rings
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Duality
Speed of electrons effects the size of rings…
Higher Anode
Voltage = Faster
Electrons
Diffraction
Rings are
smaller
The wavelength
is smaller
λ = h/mv
= h/p
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Reasons by formulae….
Mass of photon
zero!
if light are
not waves
but quanta
Work out the
root and
rearrange
Equate
Wave with
a mass?
Sub in wave
equation
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HSW - Wave nature of the electron
• Louis de Broglie (1892 - 1987)
• If light can be modeled as a particle or as a wave, can an electron
be modeled as a wave?
• The wavelength of a matter wave (1923) is given by:
• Everyday objects are too massive to give observable
wavelengths; however, electrons are light enough to give
observable wavelengths. Diffraction of electrons was observed
by two groups in 1927, Davisson & Germer and George
Thomson.
• The Bohr model could also be explained using standing waves.
• Whole numbers (1,2,3,etc.) of de Broglie wavelength give the
allowed radii found in the Bohr model.
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Energy levels explained:
The de Broglie wavelength of an orbiting electron has to fit the shape and
size the electron’s shell.
Eg for a circular orbit the circumference = n
λ
( a whole number of de Broglie wavelengths)
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The de Broglie wavelength
λ
In 1923 de Broglie hypothesised:
* Matter particles have a dual wave-particle nature
* The wave like behaviour is characterised by a wavelength
λ
=
h
mv
λ
h = Planks constant
m = mass
v = velocity
λ
=
h
p
Change the
by changing a
particle’s speed
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λ
Index
Example….
18
Use of “nu” for
frequency…
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Quantum Stuff..
TEM
(transmission electron microscope)
Electrons are accelerated to a high speed to produce a very short
de Broglie wavelength. Very detailed images can then be resolved
MRI scan
(magnetic resonance imaging)
Radio waves are emitted when hydrogen nuclei ( eg in water molecules)
change energy states in a strong magnetic field.
SQUID superconducting quantum interference device
- magnetic field detector
Used to detect very weak magnetic fields from tiny electrical currents
inside the brain and for feotal examinations
Quantum tunnelling occurs at a thin slice of an insulating barrier
placed in a superconducting ring.
When more current is induced the barrier becomes
resistive and produces a measureable voltage .
(Brian Josephson 1962 ) http://www.abdn.ac.uk/physics/case/squids.html
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De Broglie Hypothesis & KE
NB: Take a note of how this is derived....
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Question….
What is the debroglie wave
length of an electron
travelling at 3.00 x 107ms-1
Basic
What is the debroglie wave length
of an electron accelerated in a CRO
tube using a voltage of 4500V?
Harder
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Question….
What is the debroglie wave
length of an electron
travelling at 3.00 x 107ms-1
h

p
h

mv
What is the debroglie wave length
of an electron accelerated in a CRO
tube using a voltage of 4500V?
KE  qV  eV
1
eV  mv 2
2
 2eV 

 v
 m 
KE  qV  eV
1
eV  mv 2
2
2meV  m 2 v 2
2meV  mv
h

mv
h

2meV
2.43 x 10-11m
0.0183nm = 1.83 x 10-11m
Basic
Harder
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Experiments of GP Thompson
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Microstructure of Nickel Superalloys
• These pictures are taken
using electron diffraction.
They are trying to establish
the structure and if there are
any problems in the
structure of Nickel alloys
used in aeroplane
manufacture. It is important
that any micro fissures are
detected early on.
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Summary
•
We can think of electrons as waves
•
We can think of electrons as particles
•
Newtonian Mechanics works in certain cases (simple
stuff)
•
If we think of electrons in a quantum way (as waves)
the maths always works out but the calculations are
more complex
To build the structure, the scientists used a scanning tunneling
microscope (STM) to individually place 48 iron atoms on a copper
surface in a circle roughly 143 angstroms across. Then, using the STM
again to sense electron behavior inside the corral, they detected "local
densities," which appear as waves, at the very intervals predicted by
quantum mechanics -- specifically, the Schrodinger equation for a
particle in a hard-wall enclosure. The standing waves appear when iron
atoms scatter the copper's superface electrons.
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Debroglie by formulae….
Handout
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Make an A3 revision map of key points….
Ionisation?
Duality?
Excitation
(electron)
Bohr Model
Excitation
(photon)
Photoelectric
effect
Fluorescent
Tube
Quantum
Technology
Transitions
Levels
1) Formulae (basic)
2) Example Calcs (med)
3) Explanations (harder)
3 Types of
Spectrum
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Connection
•
•
•
Connect your learning to the
content of the lesson
Share the process by which the
learning will actually take place
Explore the outcomes of the
learning, emphasising why this will
be beneficial for the learner
Demonstration
• Use formative feedback – Assessment for
Learning
• Vary the groupings within the classroom
for the purpose of learning – individual;
pair; group/team; friendship; teacher
selected; single sex; mixed sex
• Offer different ways for the students to
demonstrate their understanding
• Allow the students to “show off” their
learning
Activation
Consolidation
• Construct problem-solving
challenges for the students
• Use a multi-sensory approach – VAK
• Promote a language of learning to
enable the students to talk about
their progress or obstacles to it
• Learning as an active process, so the
students aren’t passive receptors
• Structure active reflection on the lesson
content and the process of learning
• Seek transfer between “subjects”
• Review the learning from this lesson and
preview the learning for the next
• Promote ways in which the students will
remember
• A “news broadcast” approach to learning
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