[dmcoleman]

Hi, I am trying to understand the wave mechanical model for electron arrangements in atoms.  I am confused about why the electrons closest to the nucleus (n=1 level) have the least amount of energy.  From what I understand the negative electrons are attracted to the positively charged nucleus.  So shouldn't there be a greater amount of energy keeping them from touching.  It would make more sense to me if the electrons farthest from the nucleus would have less energy than the ones closest.  In other words there would have to be a greater amount of repulsive force for an electron in the 1s orbital than an electron in a 4s orbital.

[tamim83]

The thing is that electrons want to be near the nucleus since opposite charges do attract.  So the closer an electron is to its nucleus, the more stable it is.  The more stable an electron is, the lower its energy is.  So electrons that are closser to the nucleus have the lowest energy.   Electrons that are further away from the nucleus do not feel as much of the nuclear charge as the closser electrons do (i.e. 2s electrons feel less of the charge than 1s electrons).  This raises their energy as well as repuulsion from other electrons in the atom. 

Also, we tend to think of electrons in the atom as being in "bound states"  .  This means that the electron energy is negative, with zero energy being  where the electron is a very large distance from the nucleus.  So more negative energy means closer to the nucleus and more stable and "bound" to the atom. 

[dmcoleman]

I understand when you say that the closer the center of a negatively charged electron is to the singularity of the nucleus of an atom, the lesser the repulsion is.  However, there is a great deal of attractive force that is being put into play. Is it not safe to declare that we are not paying enough attention to these attractive forces?

[tamim83]

You are thinking of the electron as a particle with a charge.  Electrons are standing waves in the atom (think of a vibrating violin string twisted into a circle; but in 3D).  These waves only have certain energies, which is where the energy levels come from.  If you only think of the atom as a negative charge and a positive charge in a "classical" sense, then the electron would spiral into the nucleus giving off radiation and the atom would only last a fraction of a second.  The only way to explain why this does not happen is that electrons have "wave particle duality" , or they can behave as waves and as particles. 

[Yggdrasil]

Why don't electrons collapse into the nucleus when there is a strong attraction between the negatively-charged electrons and the positively-charged nucleus?

1)  A relatively simple explanation comes from electron-electron repulsion.  If all of the electrons in an atom were to crowd around the nucleus, you would have a lot of negative charges in a small volume.  Thus, electron-electron repulsions play some role in opposing the electron-nucleus attraction.

2)  The electron-electron repulsion idea works only in multielectron atoms, however.  What about the hydrogen atom where no electron-electron repulsions exist?  Why does the electron of a hydrogen atom not just crash into the nucleus.  The answer here has to do with quantum mechanics (essentially, the idea that electrons are waves as tamim mentioned), specifically, the Heisenberg uncertainty principle.

Briefly, the Heisenberg uncertainty principle states that one cannot know both the speed and position of a particle simultaneously.  If an electron were just to sit right next to the nucleus, the uncertainty in its position would be very small.  To compensate, the uncertainty in its speed would have to be very large.  This essentially means that the electron would be moving around very quickly and these rapid "motions" would give the electron a higher energy. 

Thus, confining an electron to a small volume actually raises its energy.  By increasing its average localizing over a larger volume of space, the electron can minimize these effects although its average distance from the nucleus will be larger.  So, in essence, there is a sort of quantum confinement "force" that opposes the electromagnetic attraction between the nucleus and electron.