De Broigle’s “waves of matter”Experimental confirmation

De Broigle’s theory of “matter waves” was nottreated 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 deBroigle “crazy prince”.

But soon all that nasty name-calling stopped!

France has a tra-dition of calling “crazy” aristocrats whose first nameis LOUIS… One of their kings is referred to in history books as “Louis the Crazy”…

What happened? In 1926, C. Davissen and L. Germer illuminateda surface of a nickel (Ni) crystal with electrons,and they observed that were strinkingly similarto those seen in X-ray diffraction…

Soon afterwards, diffraction effects were alsoobserved in experiments with electron beamspassing through thin metallic foils.

Digression: foils are most often polycrystallinesystems – they consist of a myriad of micro-crystals, i.e., of extremely small crystallinegrains 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 thinpolycrystalline foil:

X-rays

GoldThin foil

Fluorescent screen,or a photographic

plate

The X-rays willbe diffracted bygold microcrys-tals in the foil(Bragg diffrac-tion).What image willyou see on the screen?

Hint: the “microcrystals” are randomlyoriented, and there are zillions of them!

sin2 :equation Bragg - hints More fixed dn

And note that in crystals, thespacing betweenatomic planes dcan take onlydiscrete values.

Answer: a pattern of concentric rings

Screen

Here is a comparison of “transmission diffractionpatterns” 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 experimentsused to prove the wave nature of any form radiation is theYoung’s Double Slit experiment. It works for light – wouldit also work for particles? It would be the most convincingproof.” Alternatively, you can say:“The mother of all experi-ents used to prove thewave-like nature….”, etc.,is the Young’s Double Slitexperiment”.

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 1989.

Again, there are several panels in the right figure, and wewill 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 makesinterference and diffraction experiments

with electrons difficult:

Namely, the electron is a chargedparticle 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)

m.10mm 1 / maxima 100

:sensors) imaging CCDart -the-of-state (using value Realistic

m;10cm 10 :distance

screen toapparatusslit -Doublem; 10m 10 :slits

ebetween th spacing Realistic

:maxina ebetween th Separation

5

1-

5-

y

yD

d

Dyd

dDy

So, we want to use =(or longer)

1nmm10 9

Now, I want you to calculate the kinetic energy ofelectrons with de Broglie wavelength of = 1 nm

nm eV 1024.1 that know

toconvenient very sometimes isIt eV/ 100.511 massElectron

:need you will Numbersrange!energy icrelativistyet Not :Hint

find and two theCombine222

;

3

26

2222

ch

cm

Kmp

mvmmvK

ph

e

K = 1.505 eV Your result is:

Why are electrons with K=1.5 eV not particularlygood for double-slit expermiments?

Think for a moment… ANSWERThe 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 wouldyou propose?Increase the electronkinetic energy? Say,100 times? It’s easy!It would help with the“stray fields” and gasatoms. However, notethat: K-1/2

The wavelength willbe 0.1 nm now, the spacing between the maxima will decrease10 times – we may not see them any more!

Better solution: use other particles. With largermass (easier to obtain longer de Broglie waves!)and no electric charge (“stray fields” no longerpose a problem!). But are there such particles?

Yes, there are – NEUTRONS!

Double-slit interference pattern forneutrons 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 neutrondiffaction patternfrom the paper by

Zeilinger et al.

Lower panel showsthe same data in ablown-up scale toshow more clearlythe “fringes”.

Finally, a neutron diffraction pattern from a NaClcrystal (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.