Davisson-‐Germer Experiment, Thermal Neutrons, Wave Groups

Lecture 6 Davisson-­‐Germer Experiment, Thermal Neutrons, Wave Groups PHYS 302: Modern Physics
5.2 5.3
Davisson-­‐Germer Experiment 1927: direct experimental confirmation of electron wavelength…
by Davisson and Germer in U.S. and G.P. Thomson in England.
Davisson & Germer used low-speed electrons
directed at nickel target, to look at crystal
structure of nickel.
At first all they saw was reduced
intensity as ϕ increased.
(Their Ni was polycrystalline).
Then an accident caused nickel to be
oxidized: D & G heated it for long time to
reduce it … produced larger crystals.
Now the electrons were mostly hitting
single crystal, so the results were
very different…..
Results of Davisson/Germer Experiment Scattering showed large peak at one angle, caused by electron
diffraction by crystal lattice
For the graph shown, α = 90˚
ϕ = 50.0˚ at peak
V = 54.0 Volts
For constructive interference,
and d was known to be 2.15 Å, so:
Diffraction of High-­‐Energy Electron Beams Notice that the previous calculations assumed low-energy electrons.
These do not penetrate the crystal.
Single-layer diffraction.
Peaks are broad.
For high-energy, electrons are
diffracted by many layers
Peaks are narrow (or sharp spots) because
angle must be exact
(if not, some deeper layer will cancel it out)
Thermal Neutron Velocity Selector Neutrons at room temperature have wavelength comparable to crystal
atom spacings, too.
Hence used for diffraction experiments.
To get single-wavelength beam, need a velocity selector:
Electron Microscopes Transmission Electron
Microscope
Sends electrons through
sample.
Diffraction occurs.
Resulting beam is imaged
by magnetic lenses.
Resolution depends on
wavelength: much
smaller than for light.
(max: light ~ 2000
TEM ~ 1,000,000)
Usual mag. for TEM is in
range 10,000 to 100,000
Scanning Electron Microscope In SEM the electron beam is scanned across the sample, and
and reflected beam measured.
Image is then reconstructed
on a screen.
Because focus can be changed
precisely, the images can
be three dimensional.
SEM image Shown: SEM image of
single neuron.
(x 4,000)
Wave Groups De Broglie proposed wave groups
(limited in time and space)
Can make a wave group from
many waves of nearby
frequency.
Similar to beats….
Beats Traveling wave:
And since
with "phase velocity"
and
or
we can write this as:
We can superpose two waves:
But since:
We have:
Which looks like
slow envelope
×
×
high frequency wave
Group Speed vs Phase Speed The speeds of these two things (envelope and inside) are not the same!
Within the envelope:
The group (envelope):
These envelope-groups repeat.
But more isolated groups can be made by adding more waves than just
two.
With a continuous distribution of waves of nearby frequencies, can get a
single, isolated group.
(But still with distinct internal waves inside).
Homework Chapter 5, problems 1, 3, 5, 7, 9, 11.