The Bohr Model of Atomic Structure

A classical orbiting electron should radiate energy and spiral into the nucleus in a fraction of a second, the way a satellite would lose altitude if it leaked energy as it circled. Atoms obviously don't collapse like this, so something must forbid the electron from losing energy smoothly. Bohr's fix was to declare that only certain orbits are allowed at all, each with its own fixed energy. An electron sitting in one of these allowed orbits simply does not radiate. It only loses or gains energy by jumping between allowed orbits, releasing or absorbing a photon with exactly the energy difference.

The reason only certain orbits survive comes from treating the electron as a wave wrapped around the nucleus. For the wave not to cancel itself out, the orbit's circumference has to fit a whole number of wavelengths, like a jump rope that only makes a clean standing-wave pattern at certain lengths. That whole-number condition quantizes the orbit radius, and with it the energy. For hydrogen this works out to E_n = -13.6 eV / n², where n = 1, 2, 3... labels the rung of the energy ladder. The negative sign just means the electron is bound to the nucleus; n = 1 is the lowest, most tightly bound rung.

This ladder picture is exactly what the rest of the unit builds on: photon absorption and emission are jumps between these rungs, and the line spectra of atoms are the fingerprints of which jumps are allowed. The model's weakness is the literal orbit picture itself. Real quantum mechanics replaces the neat circular track with a probability cloud, no definite path at all, even though the energy levels it predicts for hydrogen still come out right.