Stability of the Classical Rutherford Atom: A Hydrogen Example

[lufc88]

I know there are other things that fail about the rutherford atom
but as the electron is accelerating and radiating away energy it would fall into the nucleus, my question is how much energy would the electron need to gain so that the classical atom could be stable
a hydrogen atom for example

 

[Nugatory]

I know there are other things that fail about the rutherford atom
but as the electron is accelerating and radiating away energy it would fall into the nucleus, my question is how much energy would the electron need to gain so that the classical atom could be stable
a hydrogen atom for example

It's not a question of how much energy the electron must gain, it's a question of how much energy must be supplied per second to make up for the energy radiated away.

You can calculate this for yourself. Use the equation for electrical attraction between two charged particles to calculate the force between electron and nucleus; use this force to calculate the necessary orbital velocity of the electron; then assume that the electron is radiating electromagnetic radiation with a frequency equal to its orbital period and amplitude equal to the diameter of its orbit.

 

[lufc88]

what equation is the energy of the em wave one that includes frequency and amplitude?

 

[Khashishi]

http://en.wikipedia.org/wiki/Larmor_formula