Difficulties with Rutherford's Model

Elegant as it was at explaining the scattering data, Rutherford's model ran into a serious theoretical problem the moment classical physics was applied to it rigorously. Maxwell's equations of electromagnetism establish that ANY accelerating electric charge must continuously radiate electromagnetic energy. An electron moving in a circular orbit is accelerating even if its speed never changes, because its DIRECTION is constantly changing -- so, according to classical electromagnetism, an orbiting electron should be radiating away energy at every instant.

This leads to a cascade of predictions, none of which match reality. As the electron radiates energy, its total energy should steadily decrease, causing the radius of its orbit to shrink continuously -- the electron should spiral inward and crash into the nucleus, and this collapse should happen almost instantly (on the order of a tiny fraction of a second) by classical estimates, meaning atoms should simply not be stable structures at all. Furthermore, as the electron spirals inward its orbital frequency (and hence the frequency of the electromagnetic radiation it emits, according to classical theory) should change continuously, so the model predicts a continuous spread of emitted frequencies, not sharp lines. …