Q:

I have heard many times that classical mechanics can't explain atoms because the electron would just spiral in. I realize there are plenty of things we need quantum mechanics to explain, but I am interested in why classical electric forces makes atoms so unstable. Consider for example gravity. On _very_ long time scales, a gravitational orbit will decay. Just as in electrodynamics, the radiation is inevitable. But this time scale is so long we can ignore it for all practical purposes. What makes electric forces so different that the classical orbits are not stable on long time scales?

- Julia Miles (age 16)

Springfield, IL, USA

- Julia Miles (age 16)

Springfield, IL, USA

A:

It's a matter of the classical electromagnetic radiation of an electron orbiting a positive nucleus. You can't ignore it. The classical lifetime is of the order of 10^{-11} seconds. See: for some gory calculations.

LeeH

One basic property enters strongly into this difference. The electrical force between two small particles (e.g. an electron and a proton) is enormously stronger than the gravitational force. This means that the orbit for electrically bound particles will have much higher acceleration than for gravitationally bound particles. The radiation power goes as the square of the acceleration. That power also goes as the square of the 'charge' so there's another reason the stronger electrical charge radiates much more than the weak gravitational 'charge'. Multiply it all out, and the gravitational radiation is under most conditions extremely weak. Its effects are measurable, however, for rotating binary pulsars (). Mike W.

LeeH

One basic property enters strongly into this difference. The electrical force between two small particles (e.g. an electron and a proton) is enormously stronger than the gravitational force. This means that the orbit for electrically bound particles will have much higher acceleration than for gravitationally bound particles. The radiation power goes as the square of the acceleration. That power also goes as the square of the 'charge' so there's another reason the stronger electrical charge radiates much more than the weak gravitational 'charge'. Multiply it all out, and the gravitational radiation is under most conditions extremely weak. Its effects are measurable, however, for rotating binary pulsars (). Mike W.

*(published on 04/19/2010)*