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How did Niels Bohr’s model explain the quantized energy levels of hydrogen?

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In 1913, Niels Bohr proposed a model of the hydrogen atom that incorporated quantum theory to explain its stability and discrete spectral lines.1

Bohr postulated that electrons could only occupy specific, allowed circular orbits of fixed size and energy, rather than the arbitrary orbits suggested by classical physics. He determined that the angular momentum of the electron is quantized, meaning it can only exist in discrete values labeled by an integer quantum number n.123

This model explains the emission and absorption of light as follows:
* Quantum Jumps: Atoms emit or absorb electromagnetic radiation only when an electron makes an abrupt transition between these allowed energy states.13
* Energy Conservation: When an electron jumps to a lower-energy orbit, it releases the difference in energy as a photon. Conversely, it must absorb a photon of the exact energy difference to jump to a higher orbit.13
* Spectroscopy: Because these orbits have discrete energies, the resulting photons have specific frequencies, which accounts for the discrete wavelengths observed in the hydrogen emission spectrum.41