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A similar dichotomy existed in the interpretation of electricity. From Benjamin Franklin’s observations of electricity in 1751 until J.J. Thomson’s discovery of the electron in 1897, electric current was seen as a flow in a continuous electric medium. Within this theory of electric fluid, the present theory of electric circuits was developed, and electromagnetism and electromagnetic induction were discovered. Thomson’s experiment showed that the unit of negative electric charge (an electron) can travel in a vacuum without any medium to carry the charge around, as in electric circuits. This discovery changed the way in which electricity is understood today and gave the electron its particle status. In Bohr’s early quantum theory of the hydrogen atom, both the electron and the proton are particles of matter. Likewise, in the Compton scattering of X-rays on electrons, the electron is a particle. On the other hand, in electron-scattering experiments on crystalline structures, the electron behaves as a wave.

A skeptic may raise a question that perhaps an electron might always be nothing more than a particle, and that the diffraction images obtained in electron-scattering experiments might be explained within some macroscopic model of a crystal and a macroscopic model of electrons coming at it like a rain of ping-pong balls. As a matter of fact, to investigate this question, we do not need a complex model of a crystal but just a couple of simple slits in a screen that is opaque to electrons. In other words, to gather convincing evidence about the nature of an electron, we need to repeat the Young double-slit experiment with electrons. If the electron is a wave, we should observe the formation of interference patterns typical for waves, such as those described in [link] , even when electrons come through the slits one by one. However, if the electron is a not a wave but a particle, the interference fringes will not be formed.

The very first double-slit experiment with a beam of electrons, performed by Claus Jönsson in Germany in 1961, demonstrated that a beam of electrons indeed forms an interference pattern, which means that electrons collectively behave as a wave. The first double-slit experiments with single electrons passing through the slits one-by-one were performed by Giulio Pozzi in 1974 in Italy and by Akira Tonomura in 1989 in Japan. They show that interference fringes are formed gradually, even when electrons pass through the slits individually. This demonstrates conclusively that electron-diffraction images are formed because of the wave nature of electrons. The results seen in double-slit experiments with electrons are illustrated by the images of the interference pattern in [link] .

Picture shows five images of computer-simulated interference fringes seen in the Young double-slit experiment with electrons. All images show the equidistantly spaced fringes. While the fringe intensity increases with the number of electrons passing through the slits, the pattern remains the same.
Computer-simulated interference fringes seen in the Young double-slit experiment with electrons. One pattern is gradually formed on the screen, regardless of whether the electrons come through the slits as a beam or individually one-by-one.

Double-slit experiment with electrons

In one experimental setup for studying interference patterns of electron waves, two slits are created in a gold-coated silicon membrane. Each slit is 62-nm wide and 4 m long, and the separation between the slits is 272 nm. The electron beam is created in an electron gun by heating a tungsten element and by accelerating the electrons across a 600-V potential. The beam is subsequently collimated using electromagnetic lenses, and the collimated beam of electrons is sent through the slits. Find the angular position of the first-order bright fringe on the viewing screen.

Strategy

Recall that the angular position θ of the n th order bright fringe that is formed in Young’s two-slit interference pattern (discussed in a previous chapter) is related to the separation, d , between the slits and to the wavelength, λ , of the incident light by the equation d sin θ = n λ , where n = 0 , ± 1 , ± 2 , . . . . The separation is given and is equal to d = 272 nm . For the first-order fringe, we take n = 1 . The only thing we now need is the wavelength of the incident electron wave.

Since the electron has been accelerated from rest across a potential difference of Δ V = 600 V , its kinetic energy is K = e Δ V = 600 eV . The rest-mass energy of the electron is E 0 = 511 keV .

We compute its de Broglie wavelength as that of a nonrelativistic electron because its kinetic energy K is much smaller than its rest energy E 0 , K E 0 .

Solution

The electron’s wavelength is

λ = h p = h 2 m e K = h 2 E 0 / c 2 K = h c 2 E 0 K = 1.241 × 10 −6 eV · m 2 ( 511 keV ) ( 600 eV ) = 0.050 nm .

This λ is used to obtain the position of the first bright fringe:

sin θ = 1 · λ d = 0.050 nm 272 nm = 0.000 184 θ = 0.010 ° .

Significance

Notice that this is also the angular resolution between two consecutive bright fringes up to about n = 1000 . For example, between the zero-order fringe and the first-order fringe, between the first-order fringe and the second-order fringe, and so on.

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Source:  OpenStax, University physics volume 3. OpenStax CNX. Nov 04, 2016 Download for free at http://cnx.org/content/col12067/1.4
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