What were the contradictions between the planetary model of the atom and the laws of classical physics?
In Rutherford’s planetary model of the atom, electrons move along circular orbits (more precisely, along curvilinear closed trajectories) with acceleration, since the direction of their velocity changes from point to point of the trajectory. According to electromagnetically and the theory, any accelerated moving electric charges (including electrons) emit electromagnetic waves. Due to radiation, the energy of electrons decreases. Losing energy, electrons approach the nucleus, their rotation frequency increases. Consequently, the frequency of the electromagnetic waves emitted by the electrons increases. In this case, the atoms must cease to exist, since the electrons, having lost their energy, must fall on the nucleus. But in reality, atoms are stable. In addition, the spectrum of an atom must contain all possible frequencies, that is, the atom must emit radiation with a continuous spectrum of frequencies. However, this result is in sharp contradiction with experience.