De Broigle’s “waves of matter” Experimental confirmation De Broigle’s theory of “matter waves” was not treated very seriously at the beginning… Some called it an interesting hypothesis with little Chance to be ever confirmed by experiments. Some other scientists called it even “crazy”. Some even called de Broigle “crazy prince”. But soon all that nasty name-calling stopped! France has a tra- dition of calling “crazy” aristocrats whose first name is LOUIS… One of their kings is referred to in history books as “Louis the Crazy”…

What happened? In 1926, C. Davissen and L. Germer illuminated a surface of a nickel (Ni) crystal with electrons, and they observed that were strinkingly similar to those seen in X-ray diffraction… Soon afterwards, diffraction effects were also observed in experiments with electron beams passing through thin metallic foils. Digression: foils are most often polycrystalline systems – they consist of a myriad of micro- crystals, i.e., of extremely small crystalline grains which are randomly oriented.

Now, a question for you: A beam of monochromatic X-rays (i.e., all of the same wavelength ) is incident on a thin polycrystalline foil: X-rays Gold Thin foil Fluorescent screen, or a photographic plate The X-rays will be diffracted by gold microcrys- tals in the foil (Bragg diffrac- tion). What image will you see on the screen? Hint: the “microcrystals” are randomly oriented, and there are zillions of them!

And note that in crystals, the spacing between atomic planes d can take only discrete values.

Answer: a pattern of concentric rings Screen

Here is a comparison of “transmission diffraction patterns” obtained using an X-ray beam (upper half) and an electron beam (lower half). (copied from K. Krane’s text, Fig. 4.3, p. 105)

One can say, however: “The archetype of all experiments used to prove the wave nature of any form radiation is the Young’s Double Slit experiment. It works for light – would it also work for particles? It would be the most convincing proof.” Alternatively, you can say: “The mother of all experi- ents used to prove the wave-like nature….”, etc., is the Young’s Double Slit experiment”. Well, it works for electrons (look at the lower panels, not the top ones, please) But why six panels? Well, it will be explained shortly. Famous result obtained at the University of Bologna, Italy (1974)

Another famous double-slit interference experiment with electrons was done in Japan in Again, there are several panels in the right figure, and we will explain in a moment what is the meaning of all that. Here is a link to an very interesting review article about double-slit experiments with electrons: The double-slit experiment - physicsworld.com

Well, but there is one fact that makes interference and diffraction experiments with electrons difficult: Namely, the electron is a charged particle of relatively small mass. But why is this a problem? OK, to explain why, let’s make some quick calculations

Realistic planning of a double-slit experiment with electrons (from the textbook, p. 68) So, we want to use = (or longer)

Now, I want you to calculate the kinetic energy of electrons with de Broglie wavelength of = 1 nm K = eVYour result is:

Why are electrons with K =1.5 eV not particularly good for double-slit expermiments? Think for a moment… ANSWER The reasons are many: ● “Stray fields” – even very weak electric or magnetic fields may considerably distort the trajec- tory of such slow electrons. ● Residual gas atoms in the apparatus vacuum chamber. The lower the is the electron energy, the higher is the pro- bability of collision with such atoms (it will become clear why when we talk about “wave packets” on Monday) What solution would you propose? Increase the electron kinetic energy? Say, 100 times? It’s easy! It would help with the “stray fields” and gas atoms. However, note that:  K -1/2 The wavelength will be 0.1 nm now, the spacing between the maxima will decrease 10 times – we may not see them any more!

Better solution: use other particles. With larger mass (easier to obtain longer de Broglie waves!) and no electric charge (“stray fields” no longer pose a problem!). But are there such particles? Yes, there are – NEUTRONS!

Double-slit interference pattern for neutrons of wavelength = 1.8 nm Copied from the original paper by Zeilinger et al. (BTW, one of the authors was C. Shull, who was awarded the 1994 Nobel Prize in Physics).

The double-slit apparatus used by Zeilinger et al.

Single-slit neutron diffaction pattern from the paper by Zeilinger et al. Lower panel shows the same data in a blown-up scale to show more clearly the “fringes”.

Finally, a neutron diffraction pattern from a NaCl crystal (such images are called “Lauegrams”, after Max von Laue, who first obtained such images using X-rays). No one expresses doubts any more that particles have a “wave-like nature” – but what does it exactly mean? It will be discussed in the next slide presentation.