This Quantum World/Serious illnesses/de Broglie

de BroglieEdit

In 1923, ten years after Bohr had derived the spectrum of atomic hydrogen by postulating the quantization of angular momentum, Louis de Broglie hit on an explanation of why the atom's angular momentum comes in multiples of   Since 1905, Einstein had argued that electromagnetic radiation itself was quantized (and not merely its emission and absorption, as Planck held). If electromagnetic waves can behave like particles (now known as photons), de Broglie reasoned, why cannot electrons behave like waves?

Suppose that the electron in a hydrogen atom is a standing wave on what has so far been thought of as the electron's circular orbit. (The crests, troughs, and nodes of a standing wave are stationary.) For such a wave to exist on a circle, the circumference of the latter must be an integral multiple of the wavelength   of the former:  

Einstein had established not only that electromagnetic radiation of frequency   comes in quanta of energy   but also that these quanta carry a momentum   Using this formula to eliminate   from the condition   one obtains   But   is just the angular momentum   of a classical electron with an orbit of radius   In this way de Broglie derived the condition   that Bohr had simply postulated.