PEP 201 Physics Laboratory
Experiment: Electron Diffraction
Instructor: Xinyu Zhao
Department of Physics and
Engineering Physics
Outline
1
Introduction about this experiment
2
Electron Diffraction and quantum mechanics
3
Experiment procedures
measuring the diameter
5
calculate the grating spacing
Comparing to the theoretical values
4
Further discussions
5
Conclusion
2.Electron Diffraction and quantum
mechanics
1900-1937 Wave-particle duality of matter
Founding fathers of quantum mechanics
A long-standing question: what is the essential of matters?
They are particles?
They are waves?
量子道
2.Electron Diffraction and quantum
mechanics
1905
By using the concept “quantum”, Einstein
explained the photoelectric effect
successfully.
Nature of
Light
Wave-like properties
e.g. diffraction,
interference
Particle-like properties
e.g. reflection
2.Electron Diffraction and quantum
mechanics
1924
De Broglie extended the Einstein’s idea, and
proposed a bolder hypotheses that not only
the light but also all the matter including the
microscopic particles like electrons, atoms or
molecules and the macroscopic object like a
rock, a car or even a person exhibits the
wave-particle duality.
h
h
 
p mv
2.Electron Diffraction and quantum
mechanics
1926
Schrödinger derived an equation to
describe the motion of this wave,
which is a basic equation in quantum
mechanics, the Schrödinger Equation.

i
  r, t   H   r, t 
t
2.Electron Diffraction and quantum
mechanics
Davisson and Thomson share the Nobel
Prize 1937 for the discovery of the electron
diffraction.
Connection-old
Connection-new
Experiment procedure
1. Connect all the equipment correctly.
2. Turn on the power.
3. Adjust the voltage from 0 to 5KV gradually.
4. Measure the diameter of each ring in the diffraction
pattern.
Dout
Din
Two types of internal spacing
Energy
conservation
De Broglie’s
wave length
1 2
mv  eVA
2

h
h

p mv
1

h

 1.23VA 2 nm
2emVa
  d sin   d

D
2L
2 L  12
d  1.23 VA
D
Image is from:
http://wanda.fiu.edu/teaching/courses/Modern_lab_manual/Electro
n_diffraction.html
Two types of internal spacing
d11
d10
Two types of internal
spacing between carbon
atoms.
Image is from:
http://wanda.fiu.edu/teaching/courses/Modern_lab_manual/Electro
n_diffraction.html
Applications of diffraction technique
Detecting micro-structure
The double hilex structure of DNA
is determined by the X-ray
diffraction technique.
Applications of diffraction
Application of electron
diffraction.
Determine the structure in
microscopic world.
The picture shows a 3-D
reconstruction of virus.
Some results from the experiment
Exp Data
Voltage (KV)
VA1/ 2
Inner (mm)
Outer (mm)
d10 (nm)
d11 (nm)
2.5
0.02
30
50.2
0.2132
0.12741
3
0.0183
28.2
49.5
0.20753
0.118229
3.5
0.0169
26.55
45.6
0.203564
0.118522
4
0.0158
24.4
43
0.207084
0.117508
4.5
0.0149
24.35
41.15
0.195689
0.115796
0.205413
0.119493
-6.17%
-2.85%
error
Further discussion
Further discussion
1. The transition from the microscopic world to the
macroscopic world
If all the objects will exhibit both the wave-like
properties and the particle-like properties, why we
can hardly find any of this effect in our daily life?
In brief, since the Plank constant is very small the
wave length of a macroscopic object will be
extremely small so that can not be detected easily.
e.g.For a person, M=100 kg V=1 m/s,
h
h
36
 
 6.63 10 m
p mv
4. Further discussion
2. Schrödinger's cat
Schrödinger's cat is a thought experiment, often
described as a paradox, devised by Austrian
physicist Erwin Schrödinger in 1935. It illustrates
what he saw as the problem of the Copenhagen
interpretation of quantum mechanics applied to
everyday objects. The thought experiment presents a
cat that might be alive or dead, depending on an
earlier random event.
4. Further discussion
Schrödinger's Cat: A cat, along with a
flask containing a poison, is placed in a
sealed box shielded against
environmentally induced quantum
decoherence. If an internal Geiger
counter detects radiation, the flask is
shattered, releasing the poison that
kills the cat. The Copenhagen
interpretation of quantum mechanics
implies that after a while, the cat is
simultaneously alive and dead. Yet,
when we look in the box, we see the cat
either alive or dead, not a mixture of
alive and dead.
4. Further discussion
Cat state in decoherence theory
 particle   g   e
 tot   g  live   e  dead
Trace the freedom of atoms, we obtain the wave function
of the cat.
 tot   live   dead
This is a superposition state, a pure state.
4. Further discussion
However, we neglect the internal freedom of the cat. In
fact the exact cat state should be written as
N
N
k 1
k 1
 tot   live   l j   dead   d j
Then we trace the internal freedom,
  Trint ernal  tot  tot

2
live live  
 *
    live dead

2
N

k 1
dead dead

l j d j  h.c. 

5. Conclusion
Conclusion
In this report, we discuss a experiment in the course PEP 201.
We show the theoretical study, the experiment procedure and
the results of the experiment. We also discuss something
interesting which is related to this experiment.
The study and discussion of this experiment will be helpful for
us to understand some fundamental issues of quantum theory
more clearly.