# Why can't an electron have a even lower energy level in atom?

by Edi
Tags: energy level
 P: 176 Why can't an electron have a even lower energy level in atom and be closer to the nuclei? (as the next step is to fuse with one of the protons and make neutron.. )
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 Quote by Edi Why can't an electron have a even lower energy level in atom and be closer to the nuclei? (as the next step is to fuse with one of the protons and make neutron.. )
You are asking why a differential equation doesn't have more solutions than it does. The answer would be analogous to the question "why is there no integer between 0 and 1?" It's not clear to me that such questions have scientific answers, and are instead probably best left to metaphysics and philosophy.
 P: 370 Well, there are limits due to the uncertainty principle. If you cram the electron closer to the nucleus you are restricting its position, so its momentum goes up accordingly and you've actually done the opposite to what you wanted. I think the opposite argument would be something like if you reduce its momentum then its position "spreads out" more, increasing the system's potential energy, so also you come undone.
 P: 615 Why can't an electron have a even lower energy level in atom? Pretty much what fzero said It's got nothing to do with quantum mechanics having some understanding of things like 'as the next step is to fuse with one of the protons and make neutron.. ' When you play about with the hydrogen atom you say that there is a point charge at r=0 that doesn't move or do anything interesting.
P: 370
 Quote by genericusrnme Pretty much what fzero said It's got nothing to do with quantum mechanics having some understanding of things like 'as the next step is to fuse with one of the protons and make neutron.. ' When you play about with the hydrogen atom you say that there is a point charge at r=0 that doesn't move or do anything interesting.
Well, that's not entirely true. An inner-shell electron CAN "fuse with one of the protons to make a neutron", it is called electron capture, but it is of course only energetically beneficial if the new nucleus has a lower ground state energy, so if you start from a nice stable nucleus you cannot lower the energy of the system this way.
P: 615
 Quote by kurros Well, that's not entirely true. An inner-shell electron CAN "fuse with one of the protons to make a neutron", it is called electron capture, but it is of course only energetically beneficial if the new nucleus has a lower ground state energy, so if you start from a nice stable nucleus you cannot lower the energy of the system this way.
I didn't say it couldn't, but that isn't built into schrodingers eigenvalue equation
P: 370
 Quote by genericusrnme I didn't say it couldn't, but that isn't built into schrodingers eigenvalue equation
Of course, but the question is about what actually happens, not just what schrodingers equation says happens. Likewise I disagree with fzero's comment that we shouldn't worry about the physical intuition behind what is going on, and should just be happy that we found a nice differential equation which gives the right answers. We'd still be stuck at the level of Newton if we decided back then that we were happy that our math described every experiment we could muster up and ignored the unsatisfactory aspects of the physical intuition behind it.
P: 615
 Quote by kurros Of course, but the question is about what actually happens, not just what schrodingers equation says happens.
Without using maths you cannot describe what 'actually' happens, people aren't from the microscopic world, we don't have the correct brains for it.

Would you argue about me using F=ma to describe and predict the motion of a cannon ball?
It's a second order differential equation, just like schrodingers eigenvalue equation.
P: 370
 Quote by genericusrnme Without using maths you cannot describe what 'actually' happens, people aren't from the microscopic world, we don't have the correct brains for it. Would you argue about me using F=ma to describe and predict the motion of a cannon ball? It's a second order differential equation, just like schrodingers eigenvalue equation.
Of course you must use math to explain what 'actually' happens, but physical intuition is extremely important for developing that math in the first place and understanding what it means.

I don't know what your point about cannonball motion is. I am not objecting to using schrodingers equation to describe electrons in atomic potentials, of course it works very well, but it is not the full story and doesn't explain the specific point raised by the OP. They were absolutely right that the energy of the total system can be lowered that way sometimes and deserved some explanation of what actually happens in that situation and why it does not occur in most atoms. Saying simply that "schrodingers equation says no" doesn't teach anyone terribly much.

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