It was during the early decades of the 19th century that the structure of atoms was coming into focus. It was known for example that a hydrogen atom contained one proton and one electron. But the scientists of the time could think of no stable arrangement of the two particles.
It was known that protons in any atom were grouped in a small central region called the nucleus and that the electrons were somehow arranged at comparatively large distances outside the nucleus. But, in hydrogen, if the electron were stationary, it would fall into the nucleus since the charges on the particles would cause them to attract one another.
Yet the electron couldnt be in an orbit circling the nucleus either. Circular motion requires constant acceleration of the circling body to keep it from flying away. But the electron has charge and charged particles radiate light when they are accelerating. So an electron in a circular orbit would radiate light and would spiral into the nucleus.
Niels Bohr proposed the first working model of the hydrogen atom. In the Bohr model, the electron circles the nucleus as if it were a planet going around the sun. And with a nod to the energy quantization that Max Planck dreamed up for solving the Ultraviolet Catastrophe, Bohr said that inside the hydrogen atom, the electron was allowed to have only discrete values of angular momentum in its orbits around the nucleus.
Translated, this means the electron can occupy orbits only at a certain distances from the nucleus. And Bohr simply dismissed the problem of the electron radiating away its energy by stating that it just didnt happen (even great scientists cheat sometimes!). He postulated that inside an atom, electrons only radiate energy when they jump from one allowable orbit to another, and the energy of this radiation, reveals the allowable orbits.
The wavelengths of light absorbed by hydrogen when white light is shined upon it, as well as the wavelengths of light when it is subsequently re-radiated had been precisely studied at the time but never explained. Here is a sample of an absorption spectrum and an emission spectrum.
By predicting the values of orbits that an electron could have, Bohrs model also predicted the wavelengths of the lines in the hydrogen spectrum. And his model was tremendously successful. It explained in exquisite detail the atomic spectra of hydrogen.
When the energy of the wavelengths of the spectral lines are compared to the energy differences in orbits allowed in the Bohr Atom they agree exactly. So the quantum approach worked well in explaining the allowable orbits, but no one was certain why only those orbits were allowed.
In his doctoral dissertation in 1924, Louis de Broglie put forward a simple idea that significantly advanced the understanding of the extremely tiny (a quantum leap forward you might say). Since Einstein and Planck and Compton had firmly established that light could have characteristics of both a wave and a particle, de Broglie suggested that matter particlesprotons, electrons, atoms, billiard balls, etc. could sometimes act like waves.
And when this idea was applied to the Bohr atom, it answered many questions. First, the allowed orbits had to be exact multiples of the wavelengths calculated for the electrons. Other orbits produced destructive interference of the waves and so the electron couldnt exist there.
So the circumference of the orbit must equal the wavelength Or twice the wavelength Or 3 times the wavelength Or, for that matter, any multiple of the wavelength. Second, these orbits werent really orbits in the traditional sense. These electrons didnt travel around the nucleus in a circle. Rather they took the form of a standing wave that surrounded the nucleus entirely. The exact position and momentum of the electron particle could not be specified at any given instant.