Brogla

Meet Brogla, a moving particle who is also a wave, with a wavelength set by her momentum.

In 1924 Louis de Broglie proposed that if light waves can act like particles, particles of matter might act like waves. He gave the rule: wavelength equals Planck's constant divided by momentum, λ = h/p. In 1927 Clinton Davisson and Lester Germer, and separately George Paget Thomson, saw electrons diffract from crystals, exactly as waves of that wavelength would.

The wavelength is tiny for everyday objects. A 0.1 kg ball moving at 10 m/s has λ around 7×10⁻³⁴ metres, far too small to detect. An electron accelerated through 100 volts, though, has λ of about 0.12 nanometres, comparable to the spacing of atoms in a crystal.

That short wavelength is why electron microscopes can resolve details far smaller than light microscopes can. Neutron and electron diffraction are used to work out the structures of materials.

De Broglie won the 1929 Nobel Prize. What the wave physically 'is' is described by quantum mechanics as a probability amplitude, not a ripple in a medium.