PARTICLES AS WAVES - de BROGLIE WAVELENGTH

Following the Compton Effect showing X-Rays behave as if they are particles with momentum, Louis de Broglie in 1923 speculated the inverse,

- if light can behave as a particle, particles should be able to behave as waves !!

- in other words, light is a member of a general family all with wave and particle properties.

Obviously this is absurd, so every one, with the VERY honorable exception of Einstein, had a good chuckle. By this time Einstein however was very famous amongst physicists and de Broglie was finally taken seriously.

He was totally vindicated when electrons were found to diffract and interfere very much as light does (in the form of X-Rays). Electrons were passed through salt crystals and the classic interference patterns found.

The above pattern is of electrons passing through a single crystal . Bright spots are antinodal, dark spaces are nodal.

For particles,

p = mv = h /λ where v = speed of particle , λ = wavelength

thus λ = h / mv for a particle eg electron

"particle like" = small wavelength

• high mass
• high velocity

eg Yourself at 60kg walking at 1ms^-1 will have a wavelength of λ = 6.63 x 10^-34 / 60 = 1.1 x 10^-34m . To "observe" this as a diffraction effect, walk through a "slit" this wide! ( Clearly you are particle-like!)

"wave like" = large wavelength

• low mass
• low velocity

eg An electron at 10⁷ms^-1 will have a wavelength of λ = 6.63 x 10^-34 / 10⁷ x 9.11 x 10^-31 m = 7.2 x 10^-11 m . This is comparable to X-Rays. Electron microscopes can "see" down to the size of an atom theoretically before diffraction effects become too large. (And they can!)

A consequence of this theory are considerable paradoxes. Young's Double Slit experiment can and has been carried out with electrons, protons, neutrons and various molecules including C60 - "buckminsterfullerene" - that extraordinary form of carbon shaped as a soccer ball.

If single objects approach a double slit, they pass through and slowly build up, one by one, the double slit pattern. Shut one slit off and they, one by one, create the single slit diffraction pattern.
Question: How do single "objects" "know" of the existence of two slits? "Clearly" they only pass through one slit! ( But if they only pass through one slit, why the two slit pattern.................HELP!!!)

This conundrum and related problems exist to this day in physics.

DeBroglie's speculation was taken up in 1925 by Erwin Schrodinger who fully developed the whole thing into QUANTUM MECHANICS.