A nucleus and an electron attract each other, so if they are to remain apart, the energy of the electron’s movement must balance the energy of attraction. However, the laws of physics had previously established that a charged particle moving in a curved path must give off energy. If this requirement is applied to an orbiting electron, why did not the electron continuously lose energy and spiral into the nucleus?
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This was one of the famous paradoxes of classical physics that was noticed in the early twentieth century and was eventually resolved by quantum mechanics. – Buzz Nov 26 '18 at 01:17
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The energy doesn’t balance. The potential energy is, on average, twice as negative as the kinetic energy is positive. The total energy is negative, meaning that the system is bound. You have to add energy in order to separate the electron from the nucleus, – G. Smith Nov 26 '18 at 01:33