What are stationary states in Niels Bohr’s atomic theory?

In Niels Bohr’s 1913 atomic model, stationary states refer to a discrete set of allowed orbits in which an electron can exist.1

Unlike classical mechanics, which suggests an infinite number of possible orbits, Bohr postulated that electrons are restricted to these specific, stable energy levels. While an electron remains in a stationary state, the atom does not emit energy as light.1

Key characteristics of these states include:

• Discrete Orbits: Electrons can only occupy orbits where their angular momentum is a whole number multiple of $\hslash$ ($\hslash =h/2\pi$).1
• Energy Transitions: Atoms absorb or emit radiation only when an electron makes an abrupt "quantum leap" or transition between these allowed states.23
• Spectral Fingerprints: Because each element possesses a unique set of energy levels, the specific frequencies of light emitted or absorbed during these transitions act as a unique identifier for that element.2

This concept was a fundamental departure from classical physics and provided the basis for understanding the line spectrum of hydrogen.13