Download Particle wavelength, Rutherford scattering

PHYS274 Spring 2017
• Quiz (iClicker reconcile beforehand)
• Homework #6 due next Friday (in a week)
– Photons  Particles
– Chap 39 in its entirety
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Q18.1
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Q18.1
Only if v = 0
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Q18.1
E = γmc2
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Q18.2
What does the “Principle of Complementarity” say
about experimental results involving light
A. We need both the wave nature and the particle
nature of light simultaneously to explain one
aspect of a single experiment.
B. We need both wave nature and particle nature to
explain all experiments but do not need both
simultaneously for one aspect of a single
experiment.
C. The principle is false, light is a wave.
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Q18.2
What does the “Principle of Complementarity” say
about experimental results involving light
A. We need both the wave nature and the particle
nature of light simultaneously to explain one
aspect of a single experiment.
B. We need both wave nature and particle nature to
explain all experiments but do not need both
simultaneously for one aspect of a single
experiment.
C. The principle is false, light is a wave.
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Q18.3
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Q18.3
Conjugate (orthogonal) variables
not bound in same way
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Q18.4
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Q18.4
E = h.f
 ∆E = h ∆f
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Goals for Chapter 39
• To study the wave nature of electrons
• To examine the evidence for the nuclear model
of the atom (Rutherford scattering)
• To understand the ideas of atomic energy levels
and the Bohr model of the hydrogen atom
• To learn the fundamental physics of how lasers
operate
• To see how the ideas of photons and atomic
energy levels explain the continuous spectrum
of light emitted by a blackbody
• To see how the Heisenberg uncertainty
principle applies to the behavior of particles
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Particles behaving as waves (another aspect of QM)
• At the end of the 19th century light was regarded as a wave
and matter as a collection of particles. Just as light was found
to have particle characteristics (photons), matter proved to
have wave characteristics.
The wave nature of matter
allows us to use electrons to
make images (e.g. the viruses
shown here on a bacterium).
This picture is the output
of an “electron
microscope”
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The Prince of Quantum Mechanics
The photoelectric effect and Compton scattering show that light waves also behave
as particles. The wave nature of light is revealed by interference - the particle
nature by the fact that light is detected as quanta: “photons”.
Photons of light have energy and momentum given by:
Prince Louis de Broglie (1923) proposed that particles also
behave as waves; i.e., for all particles there is a quantum
wave with a wavelength given by the same relation:
But be careful
c=fλ does not
Why??
work for matter
waves.
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Application of de Broglie waves
71 pm x-rays
passing through
aluminum foil;
600 eV electrons
passing through
the same.
Question: By the way, how do the 2 energies compare?
Photon: c = f.λ
Given: 71pm = λ
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Electron microscopy
• The wave aspect of electrons means
that they can be used to form images,
just as light waves can. This is the
basic idea of the electron microscope
What accelerating voltage is
needed to provide electrons
with wavelength, 10 pm =0.010
nm in an electron microscope ?
Question: The non-relativistic kinetic
energy of a point particle K=1/2mv2.
How can we rewrite in terms of p,
the momentum ?
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Electron microscope example (cont’d)
How can the accelerating
voltage be related to the
wavelength ?
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Electron microscope example (cont’d)
Question: This means that the electrons
have energies of 15keV. How does this
compare to the rest mass of the electron ?
Are the electrons non-relativistic ?
Ans: 15 keV<<511 keV, so the electrons
are non-relativistic
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Electron microscope example (conceptual question)
Question: What limits the resolution of
an optical microscope ?
Ans: the diffraction limit
What is the diffraction limit for
an electron microscope ?
Ans: Compare diffraction limit
of10 pm (0.01 nm) to 500 nm
In fact, quality of electron optics
is a worse limitation for a TEM
(transmission electron
microscope) than diffraction.
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Davisson-Germer Experiment: Electron Diffraction
In 1927, Davisson and
Germer accidentally
discover electron
diffraction at Bell Labs
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Davisson-Germer Experiment: Electron Diffraction
The diffraction maxima occur at
Question: How does electron
diffraction differ from x-ray
(Bragg) diffraction ?
Ans: 2d is twice the distance between
planes in a crystal in Bragg; here the
angle θ is measured wrt the normal.
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Rutherford’s discovery of the nucleus at Manchester
“It was quite the most incredible
event that ever happened to me in
my life. It was almost as incredible
as if you had fired a 15-inch shell at
a piece of tissue paper and it came
back and hit you.”
“Plum
pudding”
Graduate students Geiger
and Marsden carried out the
experiment.
Have you heard of Geiger ?
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Simulation: Scatter from a large nucleus
Question: What is an α particle ?
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Simulation: Hard scatter from a compact nucleus
Question: Compare to the large nucleus. What is different ?
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Rutherford scattering example
Question: An alpha particle (charge 2e) is aimed directly at a
gold nucleus (charge 79e). What minimum initial kinetic energy
must the alpha particle have to approach within 5.0 x 10-14m of
the center of the gold nucleus before reversing direction.
(Assume that the heavy gold nucleus remains at rest).
Potential energy at
distance of closest
approach. Potential at
infinity is zero.
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Rutherford scattering example (cont’d)
Question: An alpha particle (charge 2e) is aimed directly at a
gold nucleus (charge 79e). What minimum initial kinetic
energy must the alpha particle have to approach within 5.0 x
10-14m of the center of the gold nucleus before reversing
direction. (Assume that the heavy gold nucleus remains at
rest).
Potential energy at
distance of closest
approach. Potential at
infinity is zero.
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Breakdown of classical physics (Crisis)
• Rutherford’s experiment
suggested that electrons orbit
around the nucleus like a
miniature solar system.
• However, classical physics
predicts that an orbiting
electron (accelerating charge)
would emit electromagnetic
radiation and fall into the
nucleus. So classical physics
could not explain why atoms
are stable.
Question: What is the
solution to this crisis ?
There is a ground
state energy level
Why ???
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“Ultra-violet catastrophy!”
Something was very wrong
in classical physics…
Why doesn’t this happen ?
Is our universe about to end??
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“Ultra-violet catastrophy!”
Why doesn’t this happen ?
Tune in next time…
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For next time
• Particles as waves??
• Quantum Mechanics is weird!
 Read material in advance
 Concepts require wrestling with material
• Homework #6 available
– Chapter 39
– Due in a week (next Friday)
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