How did Planck’s constant contribute to Niels Bohr’s atomic model?

Planck’s constant was fundamental to Niels Bohr’s development of his 1913 atomic model, as it provided the necessary mechanism to explain atomic stability, which classical mechanics could not account for.1

Bohr realized that classical physics predicted electrons would lose energy and spiral into the nucleus. By incorporating Planck’s constant—which has dimensions of action—Bohr was able to define discrete, stable orbits for electrons. His key contributions using this constant included:1

• Quantization of Angular Momentum: Bohr postulated that an electron's angular momentum is quantized, meaning it can only exist in discrete values. This forced electrons into orbits of fixed size and energy.1
• Energy Levels: Using Einstein’s extension of Planck’s hypothesis ($E=h\nu$), Bohr determined that electrons jump between these fixed orbits by emitting or absorbing energy in discrete quanta, which explained the spectral lines of hydrogen.1
• Atomic Size: Bohr observed that when Planck’s constant is combined with the mass and charge of an electron, it produces a measure of length consistent with the known size of atoms, providing a physical basis for his model.1