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

 

[PJC01]

I would like to address the concept of stability in the Classical Rutherford Atom, specifically in the context of a hydrogen atom. While the Rutherford Atom model was a significant step in understanding atomic structure, it does have limitations and has been superseded by more accurate models such as the Bohr model and the modern quantum mechanical model.

One of the main issues with the Rutherford Atom is the lack of stability. As you mentioned, the electron in this model is constantly accelerating and radiating energy, which would eventually cause it to spiral into the nucleus. This is due to the classical laws of electromagnetism, which state that any charged particle undergoing acceleration will radiate energy. Therefore, in order for the Rutherford Atom to be stable, the electron would need to constantly gain energy to compensate for the energy lost through radiation.

To address your question about how much energy the electron would need to gain for stability, it is important to note that the Rutherford model does not take into account the quantization of energy levels in an atom. In reality, the energy of an electron in an atom is quantized, meaning it can only exist in certain discrete energy levels. This is where the Bohr model and modern quantum mechanics come into play, as they provide a more accurate understanding of the energy levels and stability of atoms.

In a hydrogen atom, the electron would need to gain an infinite amount of energy in order to maintain stability in the Rutherford model. However, in the Bohr model, the electron is confined to specific energy levels and does not radiate energy, thus providing stability to the atom. The energy required for this stability is known as the ionization energy, which is the minimum energy required to completely remove an electron from its atom.

In conclusion, while the Rutherford Atom model was a significant step in understanding the structure of atoms, it has limitations when it comes to stability. The concept of quantized energy levels in atoms is essential in understanding the stability of atoms, and the Bohr model and modern quantum mechanics provide a more accurate understanding of this concept.