Notice that we said the wavelength of an electron, not a beam of electrons. Individual electrons travel as waves, even though one would never say that individual water molecules travel as a wave like individual water waves.

The photoelectric effect (thank Albert Einstein) was telling scientists that photons behaved as if they were discrete particles with an energy proportional to their wavelength. Electrons in atoms acted as if they had discrete energy levels and could move from one to another by absorption or emission of these light particles, or photons.

Thus, electrons and photons were profoundly related. Relativity had shown (thanks again to Einstein) that you had to think of energy and momentum inthe classical world as simplifications of a more complicated relationship that applied to light as well as to matter. Relativity tied together the notions of matter and energy in a way that supported the wave nature of particles as well as the particle nature of light waves.

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