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Suppose you have a single atom, say carbon, carbon has six electrons, and six protons. Now is there anything associating the six protons locking the six electrons other than coulombic forces?

When we ionize a compound, we remove the electron from the outermost shell. Now I find this weird because, from my understanding of the Schrodinger equation, it gives orbitals which gives the probability density function of orbital as a solution. In this context, how would you explain ionization? as in supposing you ionize wouldn't the probability density functions change. What exactly are the considerations we use to describe the phenomena of ionization?

Further, the most interesting part is that the wave orbitals are distinguishable (to some extent) but not the electrons ( particle itself) why is this?

tryst with freedom
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2 Answers2

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[OP] Would this last electron, in any way, be related to the original atom and would the original atom 'want' to regain it's lost electron?

No. Individual electrons are indistinguishable. The experimental evidence goes along these lines (source: https://medium.com/physics-as-a-foreign-language/how-do-we-know-that-all-electrons-are-identical-part-2-7dad7d980dd1):

a pair of distinguishable particles which can be at 2 different locations has 4 possible states they could be in. Whereas a pair of fermions has only 1 possible state, and a pair of bosons has 3 possible states. This leads to very different statistical behavior for fermions and bosons, and explains why a lot of the properties of the 2 kinds of particles are so different.

All kinds of properties of our universe could not be explained with the current theories if electrons were distinguishable.

[OP]Further where do atomic orbitals arise from? are they a region in space having higher chance of electrons, created from having a collection of protons at a point? or are their existence independent of protons and dependent only on the electrons?

Orbitals are functions approximately describing the state of bound electrons. This description depends on where the protons are and on how many electrons there are. So they are dependent on both.

[OP, in the comments] there should be some sort of rational explanation as to why something is true.

The way science works, there is a theory or a model that is useful because it describes what has already been observed, and it makes predictions that are experimentally verified. In this sense, the state "individual electrons are indistinguishable" is true and has experimental backing. The question whether the explanations are rational or crazy is more a philosophical one. A science fiction writer probably would not have come up with quantum mechanics as a particularly reasonable theory, but it does a good job describing the reality we live in. So I would reformulate the statement above to say "there should be some experimental evidence for a model or theory used in science".

Karsten
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I asked this question way long back and with a lot more reading, I think I've come up with more specific points to answer this question.

the most interesting part is that the wave orbitals are distinguishable (to some extent) but not the electrons ( particle itself) why is this?

  • Every electron in a given atom is distinguishable in the sense that you will have a set of three quantum numbers which you can use to distinguish it from the other electrons inside that atom.

When we ionize a compound, we remove the electron from the outermost shell. Now I find this weird because, from my understanding of the Schrodinger equation, it gives orbitals which gives the probability density function of orbital as a solution. In this context, how would you explain ionization? as in supposing you ionize wouldn't the probability density functions change. What exactly are the considerations we use to describe the phenomena of ionization?

  • If the electron is given energy, it would change it quantum numbers to go up to a state of higher energy. I say 'state' instead of 'n' because there are certain cases such as the splitting of d-orbitals in certain compounds which causes the orbitals to become non degenerate. This stack post has much more detailed answers on this particular aspect.
  • Considering all the energy possible interactions in an atom, we can say that it must exist in some finite region of space using schrodinger equation. A contour of constant probability containing region which has 90% probability of finding electron are the shapes used to denote the orbitals.

The best explanation I found for this is from physics forums (here) by Jano L

So each particle is identical basically? There's no way to tell them apart?

Identical does not mean "no way to tell them apart"; that would be the meaning of "indistinguishable". Identical means the objects have the same intrinsic properties like mass, charge etc. but not location. Two xerox copies of a master blueprint are identical, yet they can be put in different places and you can tell them apart just by holding them apart each with different hand or placing them in two different rooms (and assigning different labels to the rooms). Different label means you can tell them apart and distinguish them, but they remain identical (same size, mass, color ...).

Another interesting thing I found is that, I am not the only person who found this crazy! Indeed one physicist John Wheeler came up with the idea that the explanation for all electrons being identical (here) and this PBS space time lecture

Also Refer Clayden page -84, page-86, has nice discussion on ionization and orbitals

tryst with freedom
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