# All possible energy levels

#### sridhar10chitta

Are there (available) energy levels of an electron say, at a distance 1m, or 100m or 1km away, and near the moon and beyond that belongs to an atomic nucleus on earth ?
If yes, then why does it prefer to be within the 10^-10 meter distance from the nucleus ?
Sridhar

#### Dale

Mentor
Are there (available) energy levels of an electron say, at a distance 1m, or 100m or 1km away, and near the moon and beyond that belongs to an atomic nucleus on earth ?
I believe so, but I am not certain.
If yes, then why does it prefer to be within the 10^-10 meter distance from the nucleus ?
Because that is the lowest energy state.

#### sokrates

I also believe so, but practically the electron ionizes and becomes "free" when the energies are high.

We could say, higher energy states are not "bound states" any more. If you check the probability of finding the electron measured from the center of the hydrogen atom, it decays exponentially with the distance for low energy "bound states" , but the peak of the curve shifts to the right when the energy increases.

Check the following and see what happens as "n" increases ( Increasing n - is increasing the energy)

http://hyperphysics.phy-astr.gsu.edu/Hbase/hydwf.html

#### alxm

The nucleus has an opposite charge, so the electron is attracted to the nucleus and gains potential energy from being located closer to it. On the other hand, by 'confining' itself to a smaller region of space, it increases its kinetic energy (c.f. particle-in-the-box).

So if $$Z \rightarrow 0$$ the electron will spread out over all space, and as $$Z \rightarrow \infty$$ the electron becomes entirely concentrated at the nucleus.

The 10^-10 m value happens to be where these two effects balance out.

#### tiny-tim

Homework Helper
Hi sridhar10chitta!
Are there (available) energy levels of an electron say, at a distance 1m, or 100m or 1km away, and near the moon and beyond that belongs to an atomic nucleus on earth ?
I think the main problem is that at 1m away, that won't be the only nearby nucleus … the energy levels depend on the total field, which is the equivalent of Z -> ∞.

But if a nucleus were completely isolated, in some void in space, then energy levels far beyond the usual would be available.

In other words, if a really energetic photon hits an electron "orbiting" a nucleus on Earth, there's no energy level round the same nucleus for it to go to (so I suppose it just "escapes"), but in a void in space, the same photon could knock the electron out to a huge distance, and it would still be "orbiting".

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