The de Broglie Wavelength

Light behaves like a wave and like a particle. De Broglie's idea, proposed in 1924, was to flip that around: if waves can act like particles, maybe particles can act like waves. He proposed that any moving object has a wavelength tied to its momentum, lambda = h/p, where p = mv and h is Planck's constant, 6.63 x 10⁻³⁴ J s. Double the momentum and the wavelength is cut in half. This is not a metaphor. Electrons genuinely diffract and interfere, just like light passing through a slit.

The reason nobody notices a baseball's wavelength is the size of h. Planck's constant is tiny, so unless mv is also tiny, lambda comes out far smaller than anything you could ever detect with a ruler, a slit, or any physical apparatus. An electron has a mass around 9.11 x 10⁻³¹ kg, small enough that even at ordinary speeds its wavelength lands in the range of atomic spacing, roughly 10⁻¹⁰ to 10⁻⁹ meters. That is why electron waves show up in real experiments and baseball waves never do.

This sets up the rest of modern physics. Once you accept that electrons have wavelengths, it makes sense that they can only exist in certain standing-wave patterns around a nucleus, which is exactly the energy-level picture used for atomic spectra. It also explains the electron microscope, which trades light for electrons to resolve far smaller structures than any optical microscope could ever manage.