Stability of the Classical Rutherford Atom: A Hydrogen Example

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Discussion Overview

The discussion revolves around the stability of the classical Rutherford atom, specifically using the hydrogen atom as an example. Participants explore the implications of an accelerating electron radiating energy and the conditions under which the classical model could be considered stable.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • One participant questions how much energy an electron would need to gain for the classical Rutherford atom to be stable, considering the electron's tendency to fall into the nucleus due to energy loss from radiation.
  • Another participant suggests that the focus should be on the energy that must be supplied per second to compensate for the energy radiated away, rather than a one-time energy gain.
  • A participant asks for clarification on the equation related to the energy of electromagnetic waves, specifically one that includes frequency and amplitude.
  • A link to the Larmor formula is provided, which may relate to the discussion on energy radiation from accelerating charges.

Areas of Agreement / Disagreement

Participants express differing views on the nature of energy requirements for stability, with no consensus reached on the specifics of the energy calculations or the implications for the Rutherford model.

Contextual Notes

The discussion does not resolve the assumptions regarding the classical model's limitations or the specific calculations needed to determine energy requirements.

lufc88
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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
 
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lufc88 said:
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.
 
what equation is the energy of the em wave one that includes frequency and amplitude?
 

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