How did Planck’s constant help explain quantized electron orbits?

Max Planck’s constant ($h$) was instrumental in the development of the Bohr model of the atom, providing the mathematical foundation to explain why electrons occupy discrete, stable orbits rather than spiraling into the nucleus as classical physics predicted.12

In 1913, Niels Bohr utilized Planck’s constant to resolve the instability of the Rutherford model. His key contributions included:

• Quantization of Angular Momentum: Bohr postulated that an electron’s angular momentum is restricted to discrete values, specifically whole-number multiples of the reduced Planck’s constant, $\hslash$ ($\hslash =h/2\pi$).13
• Stationary States: By applying this quantization, Bohr defined specific, allowed orbits of fixed size and energy. Because these orbits are quantized, electrons cannot lose energy continuously; they remain in stable, nonradiating states.12
• Energy Transitions: Bohr determined that radiation is only emitted or absorbed when an electron jumps between these discrete orbits. The energy of the emitted or absorbed photon corresponds exactly to the difference in energy between the two orbits, a relationship governed by the frequency of the radiation and Planck’s constant ($E=h\nu$).12

These applications of Planck’s constant successfully explained the discrete line spectrum of hydrogen.12