Every moving object — an electron, a baseball, you — has a wavelength, λ = h / (mass × speed). For a baseball it’s absurdly tiny and you never notice; for a slow electron it’s atom-sized, which is why electrons DIFFRACT and electron microscopes work. A length that falls out of momentum. Slide the speed and watch the wavelength swing.
The de Broglie wavelength λ = h/p = h/(mv) assigns a wave to any particle of momentum p. Faster (or heavier) means shorter wavelength; it is why a slow electron (λ ~ 10⁻⁹–10⁻¹⁰ m) diffracts off a crystal like light off a grating, while a baseball’s λ (~10⁻³⁴ m) is unobservable. De Broglie’s 1924 hypothesis, confirmed by Davisson–Germer. A fail-loud self-check throws unless an electron at ~10⁶ m/s yields λ of order 10⁻⁹–10⁻¹⁰ m. ◆ real physics, node-verified.
Non-relativistic λ=h/mv is exact in that regime; near light-speed the relativistic momentum is needed. The wavelength is real (it diffracts); picturing a localized particle AS a spread wave is the usual interpretive caution.