A new picture of the atom thus emerged, in which all the positive charge and virtually all the mass was concentrated in a tiny NUCLEUS at the centre of the atom and the light, negatively charged ELECTRONS orbited about it at rather large distances, much like the Earth and other planets about the Sun. This is a compelling and pretty image, and there is no problem calculating the orbital velocities of the electrons in the attractive central force of the nucleus.
The problem is, the accelerations of said electrons are enormous, causing them to radiate away their energy as electromagnetic waves (light) and spiral down into the nucleus. The lifetime of such an atom must be less than about 1 ns (or 10-9 seconds), during which time the atom gives off a bright pulse of light. Then, nothing.
This doesn't quite fit the data. Atoms are apparently quite stable and we are still here to talk about it, so there must be something wrong with this picture. Naturally, armies of Physicists went to work trying to find fault with the logic of classical electrodynamics, but there was no way out; the predictions were too simple to be mistaken. Something was seriously wrong.