Dual Nature of Matter and Light: de Broglie's Relationship

By the early 1920s, the photoelectric effect had already forced physicists to accept that light -- long understood purely as a wave, on the strength of interference and diffraction experiments -- also behaves as a stream of discrete energy packets called photons, each carrying energy $E = h\nu$ and momentum $p = h/\lambda$. Light, in other words, shows a dual nature: it behaves as a wave in some experiments and as a particle in others.

De Broglie's hypothesis. In 1924, Louis de Broglie proposed a strikingly symmetric idea: if a wave (light) can behave like a particle, then a particle (matter) should equally be able to behave like a wave. He suggested that every moving particle of mass $m$ and velocity $v$ has an associated wavelength, now called the de Broglie wavelength, given by combining the photon relations above:

where $h$ is Planck's constant and $p = mv$ is the particle's momentum. This relation applies, in principle, to every moving object -- a thrown ball, a car, an electron -- but Planck's constant is so small ($6.626 \times 10^{-34}\ \text{J s}$) that for any macroscopic object (large mass, ordinary speed) the resulting wavelength is many orders of magnitude smaller than the object itself, so its wave nature is completely unobservable in practice. For a very light particle moving at high speed, such as an electron, however, the de Broglie wavelength comes out comparable to atomic dimensions or to X-ray wavelengths, and its wave character becomes experimentally significant. …