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Introduction
The electron diffraction tube consists of an electron gun that accelerates electrons towards a graphite foil. In contrast to the cathode ray tube and the fine beam tube a much higher voltage is used, why the wave behaviour of the particles outcrop: the electrons are diffracted at the inner structure of the graphite.
Functional principle
- The source of the electron beam is the electron gun, which produces a stream of electrons through thermionic emission at the heated cathode and focuses it into a thin beam by the control grid (or “Wehnelt cylinder”).
- A strong electric field (10 kV!) between cathode and anode accelerates the electrons, before they leave the electron gun through the spaces of the anode-grid.
- Afterwards the accelerated electrons hit a thin graphite foil. The electrons are diffracted there so they fly towards the screen in different directions.
- When electrons strike the fluorescent screen, light is emitted so that the diffraction picture gets visible.
- The whole configuration is placed in a vacuum tube to avoid collisions between electrons and gas molecules of the air, which would attenuate the beam.
UA
Cathode
Control grid Anode
Flourescent screen
Graphite foil
Setup
Equipment Assembling the experiment
1 Electron diffraction tube 1 DC power supply 1 High voltage supply unit (0..10kV) Cables
- Connect the sockets of the electron diffraction tube to the power supply as shown in the circuit diagram below.
- Connect the high voltage to the anode G3 through a 10 MΩ protective resistor (the resistor can be cancelled if the high voltage power supply unit includes a current leveller like the one at teachers lab).
Wave behaviour of the electron
Tasks:
- Build up the experimental setup (see “setup”) and observe the diffraction picture on the screen!
- Measure the radii r of the first and the second ring und work out the wavelength of the electrons! Information: - The optical retardation between light reflected at neighbouring planes (distance: d) of the carbon
atoms is δ = 2 ⋅ d ⋅sin θ (see draft).
Constructive interference occurs if the optical retardation is a multiple of the wavelength λ, that’s why for maxima (brightly rings at the
screen) it is n ⋅ λ = 2 ⋅ d ⋅sin θ.
- The diffraction angle θ can be calculated by the radius r of the maxima and the distance D=127mm between screen and graphite foil through geometrical reasons (for further information, see PHYWE 25113-00) with:
D
2 r
arcsin
- The distance between the two relevant planes of the carbon atoms is d 1 =213 pm and d 2 = pm.
- Compare your result to the wavelength that is given by deBroglie equation λ=h/p!
UA
D
2 Θ^ r
Results:
- Electrons behaving like particles would not case a diffraction picture when passing matter like the graphite foil. Since a diffraction picture gets visible, there is diffraction – electrons behave like waves.
After Einstein introduced the duality of wave and particle behaviour of light first in 1905, deBroglie proposed 1924 that not only light has both wave and particle behaviour: matter, so far seen as consisting of particles, should behave like waves as well, which can be verified with this experiment in the electron diffraction tube
- Measuring the radii r 1 und r 2 and working out the corresponding wavelengths we have a wavelength of λ=12 pm at 10 kV acceleration voltage.
- DeBroglie posited the formula λ=h/p for the wavelength of matter. The impulse p of the electrons in the electron diffraction tube depends on the acceleration voltage U:
eU p e m U
m
p
Ekin = m ⋅ v = e ⋅ U ⇒ = 2 ⋅ ⋅ ⇒ = 2 ⋅ ⋅ ⋅
With deBroglie equation we have for U=10 kV:
pm
e mU
h
p
h 12 , 29
This is almost the same as the experimental result from (2.), whereby deBroglie’s hypothesis of „matter waves “ and his formula to compute their wavelength are confirmed experimentally.
- At low energy there is no diffraction image on the screen. The reason is that deBroglie wavelength of
with 300 V accelerated particles is only pm
e mU
h
p
h 70 , 83
λ = = which is too much to
analyse the distance between the lattice planes of graphite that is d 1 =213 pm and d 2 =123 pm.
To analyse the inner structure of matter, the bullet particles have to be as small as possible compared to the analysed structure. Light with a wavelength of λ=500 nm e.g. is not appropriate to analyse the planes of a graphite foil whose distance is only d = 213pm. That’s why light-optical microscopes are not useful to analyse the planes of graphite because the wavelength is much bigger than the structure. The deBroglie wavelength of 10 kV electrons is about 12 pm (see above) so they allow the study of the inner structure of graphite.
In summary bullet particles for scattering experiments have to be very small to get a good resolution. Since deBroglie wavelength λ=h/p is inversely proportional to the impulse p, scattering experiments need strong particle accelerators. This is the reason why the electron diffraction tube needs a high voltage of at least 10 kV.
Well-known scattering experiments
Year Experiment Bullet particles Cognitions
1908 Rutherford α-particles Discovery of the atomic nucleus
1956 Hofstadter Electrons Size of a proton
1962 Friedman, Kendall, Taylor Electrons Proof of the existence of quarks
1992 HERA Electrons, muons, neutrinos Structure of protons
Proton
Electron
Scattering experiment to prove the existence of quarks
