What forces the 3rd electron to form a 2s state?

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Discussion Overview

The discussion revolves around the question of why the third electron in a lithium ion (Li 1+) occupies a 2s state after ionization, focusing on the forces and principles that govern electron configuration in atomic structure. The scope includes theoretical explanations related to quantum mechanics, electron interactions, and the implications of the Pauli Exclusion Principle.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • Some participants propose that the placement of the third electron into a 2s state is due to the need to fill orbitals for a more stable, lower potential energy configuration.
  • Others argue that the Pauli Exclusion Principle prevents more than two electrons from occupying the 1s state, necessitating the placement of the third electron in the 2s state.
  • A participant questions the forces that drive the placement of the third electron, seeking clarification beyond the principles of quantum mechanics.
  • Another participant explains that there is no classical force associated with the Pauli principle, but rather a fundamental restriction based on the nature of fermions and the requirement for anti-symmetrization of wave functions.
  • Some contributions mention the role of Coulombic interactions and the magnetic dipole moment of electrons in determining energy levels, while others emphasize the independence of electrons in the context of quantum mechanics.
  • One participant highlights that the lowest energy configurations are determined by the Coulomb central force model and the neglect of electron-electron interactions.

Areas of Agreement / Disagreement

Participants express differing views on the nature of the forces involved in electron placement, with some focusing on quantum mechanical principles and others on classical interpretations. The discussion remains unresolved regarding the specific forces at play in the electron configuration of lithium.

Contextual Notes

Limitations include the complexity of electron interactions, the dependence on quantum mechanical principles, and the varying interpretations of the Pauli Exclusion Principle and Coulombic forces.

what_are_electrons
[SOLVED] What forces the 3rd electron to form a 2s state?

Helium can handle two electrons as long as the spin of one is opposite to the other. Lithium has 3 electrons, 3 protons and 3 neutrons. If one electron is ionized producing a 1+ ion, and it is then exposed to a source of low energy electrons, why does Li (1+) add the "new" electron to a 2s state? What forces are at work?
 
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what_are_electrons said:
Helium can handle two electrons as long as the spin of one is opposite to the other. Lithium has 3 electrons, 3 protons and 3 neutrons. If one electron is ionized producing a 1+ ion, and it is then exposed to a source of low energy electrons, why does Li (1+) add the "new" electron to a 2s state? What forces are at work?

When you ionize an atom, the electron has to overcome the potential barrier coming from the presence of the atomic nucleus. This is a mere coulombic interaction. You will also need to incorporate the coulombic interaction of the electron with other electrons.

The Li(1+)-state will add an electron in order to fill up the orbitals. Basically this corresponds to a more stable state of lower potential energy


regards
marlon
 
what_are_electrons said:
Helium can handle two electrons as long as the spin of one is opposite to the other. Lithium has 3 electrons, 3 protons and 3 neutrons. If one electron is ionized producing a 1+ ion, and it is then exposed to a source of low energy electrons, why does Li (1+) add the "new" electron to a 2s state? What forces are at work?

Hadn't it been for the Pauli's wonderful job,the Li ion 1+ would add the electron to the lower energy (hence more stable) 1s.Unfortunately/fortunately (depends on what your viewpoint is),the principle of Pauli tells us there cannot be more than 2 electrons in the 1s state...Since the state available with the lowest energy is 2s,then the electron would have to go to 2s...Simple...

Daniel.
 
Sorry, I was not clear about my question. What forces the 3rd electron to occupy a new level?
 
what_are_electrons said:
Sorry, I was not clear about my question. What forces the 3rd electron to occupy a new level?

Did u read my post??Please indicate what u found unclear.I believe i answered your question... :rolleyes:

Daniel.
 
dextercioby said:
Did u read my post??Please indicate what u found unclear.I believe i answered your question... :rolleyes:

Daniel.

Yes, I read your post. Yes, I understand that the placement of the 3rd electron into a new state is a lower energy state, but PEP unfortunately does not include any info about the forces that drive the placement of the 3rd electron. PEP is a prediction tool, not a force. I hope to understand what sort of forces push the electron to occupy that new lower energy state. Suggestions?
 
To really understand this you will have to first learn some basic quantum mechanics; understand what symmetric and anti-symmetric wavefunctions are; as well as what fermions and bosons are.
 
Gokul43201 said:
To really understand this you will have to first learn some basic quantum mechanics; understand what symmetric and anti-symmetric wavefunctions are; as well as what fermions and bosons are.

Have already taken basic QM 'bout 20 yrs ago, and understand sym and anti-sym wave functions as well as fermions and bosons. With that out of the way, what's next?
 
HUND'S RULES AND THE CONSTRUCTION OF THE ELECTRON CONFIGURATIONS IN THE PERIODIC TABLE OF ELEMENTS...

Daniel.
 
  • #10
dextercioby said:
HUND'S RULES AND THE CONSTRUCTION OF THE ELECTRON CONFIGURATIONS IN THE PERIODIC TABLE OF ELEMENTS...

Daniel.

Been there, done that, now what?
By the way, do you have any clue what drives Hund's rule? I have an idea, but it is one of those forbidden theories, so I can't tell you less I be doomed to theory land.
 
  • #11
I think I see the answer being sought: an explanation of HOW and WHY the Pauli principle works. Let's address those in turn.

HOW: There is NO (classical) force associated with the Pauli principle. Let's take a simple example, two identical non-interacting spin-1/2 particles in a box. It is a very simple exercise to show that if you anti-symmetrize and try to put them both in the same state, your wave functions go to zero. It can't be done, NOT because of some force keeping them apart, but because the particles cannot exist in that manner; it is forbidden by their very nature (assuming the wave mechanics description is correct). However, in many-particle cases where there are many identical fermions and the state density is high, the behavior can be effectively described as a repulsive force that prevents further compression. Solid state physicists or astrophysicists can explain this much better than I.

As to WHY the Pauli principle applies, this is a result from field theory. It can be shown that particles that are quanta of the same field must be described by either symmetric or anti-symmetric wave functions. Furthermore, if you take a field whose quanta have spin-1/2 and apply the QFT quantization rules, you find that only anti-symmetric wave functions produce acceptable results. Specifically, symmetric wavefunctions for a field with half-integer spin result in a breakdown of causality.
 
  • #12
what_are_electrons said:
By the way, do you have any clue what drives Hund's rule?


Quantummechanics


marlon
 
  • #13
what_are_electrons said:
I hope to understand what sort of forces push the electron to occupy that new lower energy state. Suggestions?


The answer comes from QM. Now, since you took this subject you will know what i am talking about since it is very elementary. You know the "naive" model of electrons orbiting some atomic nucleus and having an intrinsic spin-moment (the spin s). Now, given the fact both these quantumnumbers are directly related to the magnetization (a circular current is equivalent to a magnetic dipole), there is another way to look at things : when electrons fill up certain energy-levels AND the potential energy must be as low as possible, one can also talk about keeping the potential energy of some dipole submerged in some magnetic field (coming from the nucleus in this case) as low as possible. QM provides the tools to work with energy? Indeed, it is thanks to the interaction of the electron with the nucleus and other electrons that the energy-levels for L and S exist. These energy-levels are no inherent property of one electron (this is a popular misconception), however they only arise because the electron is affected in a certain way by the presence of the atomic nucleus. How it is affected is expressed in terms of energy-levels or energy-states.

So to conclude, if we are able to talk about potential energy, then we are also able to talk about force no ? The force at hand comes from the dipole inside a magnetic field. Just look at spin-flips for example...

regards
marlon
 
  • #14
Got it. Many thanks! It's what I was understanding, but I wanted some confirmation.
 
  • #15
what_are_electrons said:
Got it. Many thanks! It's what I was understanding, but I wanted some confirmation.


no problem...my pleasure

marlon
 
  • #16
But, that's not exactly what's going on. Magnetism has zip to do with the placement of electrons into orbitals, for the basic lithium structure in question. (If I have misunderstood, please accept my aplogies.)The three keys are:

the Coloumb central force model of the atom,
The Pauli Exclusion Principle
The neglect of electron-electron interactions.

QM then determines that the problem is seperable, and each electron can be treated independently of the others-as far as finding wave functions is concerned. The lowest Coloumb levels are 1S and 2S. When ionized, the Lithium will end up with two electrons, spin up and spin down, in the 1S state. Actually, the PEP says: each electron has an equal probability of being spin up or spin down, which follows from the antisymmetry of the wave function. Most importantly, there is no room in the 1S state for another electron. So, the minimum energy configuration is 2 in the 1S state and one in the 2S -- except, of course, the PEP says that each charge has a probability to be found in the 1S +, 1S -, 2S +, 2S - states.

The PEP is, at first glance, not a force. BUT, in classical mechanics we talk about forces of constraint-- with, for example, a ball rolling off a table --. I've never seen it done, but I'm quite sure that in a Lagrangian formulation of QM, both Bose-Einstein and Fermi-Dirac statistical requirments of symmetry, and antisymmetry, could be formulated as constriants expressed in the Lagrange Multiplier formalism. Then go to Lanczos, The Variational Principles of Mechanics, for his lucid discussion of the interpretation of Lagrange Multipliers in terms of forces.

Regards,
Reilly Atkinson
 
  • #17
reilly said:
But, that's not exactly what's going on. Magnetism has zip to do with the placement of electrons into orbitals, for the basic lithium structure in question. (If I have misunderstood, please accept my aplogies.)

I disagree with this statement, to some extent. The possible energy-levels for an electron to occupy DO come from the fact that this atom is "bound" to an atomic nucleus. They are not inherent to the electron itself, i mean : e free elecrton won't occupy a p-orbital for example.

In QM, it is quite clear and straightforeward to make a connection between magnetic dipoles and magnetization more genereally and the L and S operators. I don't think you won't deny this and that was my original point

regards
marlon
 
  • #18
Can somebody explain how electron spin? It is caused by magnetic field of the nucleus?
 

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