How did Niels Bohr explain the hydrogen spectrum?

In 1913, Niels Bohr proposed a model of the hydrogen atom that successfully explained its discrete line spectrum by incorporating quantum theory into the existing Rutherford model.21

Bohr postulated that electrons could only occupy a discrete set of circular orbits, known as stationary states, where they do not radiate energy. He assumed that an electron's angular momentum in these orbits must be a whole-number multiple of $\hslash$ ($\hslash =h/2\pi$).21

According to Bohr, light is emitted or absorbed only when an electron makes an abrupt transition between these allowed energy states. The frequency $\nu$ of the emitted or absorbed radiation is determined by the energy difference between the initial and final states:21
$$\nu =|E_m-E_n|/h$$
By applying these assumptions, Bohr derived the mathematical formula for the wavelengths of hydrogen's spectral lines, correctly calculating the Rydberg constant and providing a theoretical basis for empirical observations like the Balmer series.31