The Bohr-de Broglie model was a brilliant and original insight into how electrons perform within the atom. De Broglie proposed that just as light had been shown to have both a wave and a particle aspect, so might matter.
His now famous wave equation, indicated that an electron in a Bohr orbit racing around the atom's nucleus would possess a wavelength of the right dimension to form standing waves. He envisioned the orbit as a pilot wave -- continuous along the electron's path. It was like a vibrating string -- where whole, identical waves are formed. In his picture, the electron must "remember" where it had been as well as where it was going on Bohr's energy spheres.
As in the illustration at right, he showed that one standing wave could fit into the first shell, like a snake grabbing its tail. Two could form in the second shell, three in the third, etc.
As in Bohr's model, de Broglie's electron could move from one shell to another, through varying electrical levels, only by performing electrical work. This means taking in or giving off light. Normally the electron stayed on a shell at a constant distance from the nucleus.
As the shells and orbits of Bohr's model are quantized, so is the length of the wave of de Broglie's electron at each shell. It grows longer as the electron moves to shells farther from the nucleus. This is because the electron travels more slowly in the larger shells, just as planets do in orbits more distant from the sun.