In 1924, Louis de Broglie proposed that every particle of matter, not just light, has an associated wavelength λ = h/p. This simulation lets you sweep the mass and speed of a "particle" from an electron to a baseball and watch the predicted wavelength change by more than thirty orders of magnitude. The idea was confirmed experimentally in 1927 by Davisson and Germer, who fired electrons at a nickel crystal and observed diffraction — direct proof that electrons behave as waves. The same wave nature is put to practical use in electron microscopes, where sub-nanometre electron wavelengths resolve individual atoms far beyond the reach of visible-light optics.
λ = h/p = h/(mv), with Planck's constant
h = 6.626×10⁻³⁴ J·s. The dimensionless ratio λ/d (wavelength over
slit separation) is the diffraction-visibility criterion: fringes
are only observable when λ/d is not vanishingly small compared to
the aperture.
In 1999, Anton Zeilinger's group in Vienna fired C60 "buckyball" molecules — nearly a nanometre across and made of 60 carbon atoms — through a diffraction grating and recorded a genuine matter-wave interference pattern, extending de Broglie's hypothesis to one of the largest objects ever shown to behave quantum mechanically.
In 1924 Louis de Broglie made a bold symmetry argument: if light, normally described as a wave, can behave as particles (photons), then particles of matter should also have a wave nature. He proposed that any particle with momentum p = mv carries an associated wavelength λ = h/p, where h is Planck's constant. This idea seemed outlandish at the time, yet it was confirmed just three years later by Clinton Davisson and Lester Germer, who scattered electrons off a nickel crystal and observed a diffraction pattern that only waves can produce.
This simulation lets you explore that relationship directly: as mass and speed change, the computed wavelength λ = h/(mv) shifts across more than thirty orders of magnitude, from picometre-scale electron waves down to a hopelessly small wavelength for a thrown baseball. The double-slit feasibility panel converts this into something you can see — when λ/d is large enough, sharp interference fringes appear; for any everyday object λ/d is astronomically small, so no wave behaviour is ever observed. This exact wave nature of electrons is exploited in electron microscopy, where wavelengths thousands of times shorter than visible light let scientists resolve individual atoms.
It is the wavelength λ = h/p = h/(mv) associated with any moving particle, where h is Planck's constant (6.626×10⁻³⁴ J·s), m is the particle's mass and v its velocity. De Broglie proposed in 1924 that this wave nature applies to all matter, not just light, extending wave-particle duality to electrons, atoms and, in principle, any object.
A baseball's mass is enormous compared to an electron's, so even at typical throwing speeds its de Broglie wavelength works out to roughly 10⁻³⁽ metres — vastly smaller than an atomic nucleus and utterly undetectable. The ratio λ/d against any realistic slit separation is so close to zero that the resulting interference fringes would be spaced far below the width of a single atom, which is why macroscopic wave behaviour is never observed in daily life.
In 1927, Clinton Davisson and Lester Germer fired a beam of electrons at a nickel crystal and measured the electrons scattering at specific angles that matched the diffraction pattern predicted for waves of wavelength λ = h/(mv). This was direct experimental confirmation of de Broglie's hypothesis and earned Davisson a share of the 1937 Nobel Prize in Physics.
Fast electrons in an electron microscope have de Broglie wavelengths thousands of times shorter than visible light — often just a few picometres. Because the resolving power of any microscope is limited by the wavelength it uses, these tiny electron wavelengths let electron microscopes image individual atoms, far beyond what light microscopes can ever achieve.