the de Broglie wavelength
/ duh BROY /
The de Broglie wavelength is the wavelength that any moving piece of matter, an electron, an atom, even a thrown baseball, carries as its hidden wave. Everyday image: if light can act like particles (photons), then, argued Louis de Broglie in 1924, particles ought to act like waves, and every moving object should have a wavelength. The question it answers is: how long is that wave, and why do we never see a cricket ball ripple?
Precisely, the de Broglie wavelength equals Planck's constant divided by the object's momentum: lambda = h / p, where p = m v for a slow object (mass times velocity) and h is Planck's constant. Because h is so tiny (about 6.63 x 10^-34 J s), a heavy or fast object has an enormous momentum and therefore a wavelength far too small to ever notice. Only very light, slow things like electrons have a wavelength big enough to reveal wave behaviour such as diffraction.
Why it matters: de Broglie's guess was confirmed within three years when electrons fired at a crystal produced a diffraction pattern, exactly as waves would. This is the working principle of the electron microscope, which uses the short wavelength of fast electrons to see far finer detail than light ever could. Honest caveat: a baseball does have a de Broglie wavelength, but it is around 10^-34 metres, unimaginably smaller than an atom, so its wave nature is utterly undetectable, which is why the everyday world looks solidly particle-like.
An electron accelerated through 100 volts has a de Broglie wavelength of about 0.12 nanometres, comparable to the spacing between atoms in a crystal, which is exactly why such electrons diffract off crystals and let us image atoms.
Slow electrons have atom-sized wavelengths; baseballs do not.
Everything has a de Broglie wavelength, but for macroscopic objects it is fantastically small, which is why wave behaviour shows up only for tiny, light particles.