Question about electrons per shell

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    Electrons Per Shell
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Discussion Overview

The discussion revolves around the maximum number of electrons that can occupy atomic shells, specifically questioning the established sequence of 2, 8, 18, 32, and 50 electrons per shell. Participants explore the mathematical and theoretical underpinnings of this distribution, including references to quantum mechanics and the Pauli exclusion principle.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant questions why the maximum electrons per shell follow the pattern of 2, 8, 18, 32, 50, suggesting that a sequence of 2, 8, 16, 32, 50 might be more mathematically appealing.
  • Another participant explains that the maximum number of electrons is determined by the degeneracy of energy shells and the Pauli exclusion principle, detailing how the number of orbitals increases with higher energy levels.
  • The explanation includes specific orbital counts for shells n=1 through n=3, indicating that each orbital can hold two electrons due to the Pauli principle.
  • A participant raises a hypothetical question about the possibility of having 71.5 electrons in the n=6 shell, which is met with skepticism regarding the feasibility of such a scenario.
  • Another participant humorously responds to the previous question, implying the absurdity of splitting an electron.
  • A later post mentions that the nucleus also has shells and subshells, suggesting additional complexity in the atomic structure.

Areas of Agreement / Disagreement

Participants express differing views on the mathematical representation of electron distribution in shells, with no consensus reached on the proposed alternative sequence. The discussion includes speculative elements regarding the feasibility of certain electron counts, indicating a lack of agreement on those points as well.

Contextual Notes

The discussion does not resolve the mathematical assumptions behind the electron shell configurations, nor does it clarify the implications of the nucleus's shells and subshells on the overall topic.

nuby
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why is it the maximum electrons per shell is 2,8,18,32,50 ... Wouldn't 2,8,16,32,50 make more sense mathematically?

Are there any equations the show why this occurs?
 
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It is due, first due to the degeneracy of the energy shell (i.e. how many energy states that have that shell's energy) and also due to the pauli exclusion principle.

First, the higher energy shells have bigger degeneracies. In simple terms, there are more orbitals in the n=2 shell than there are in the n=1 energy shell. Thus, they can hold more electrons. Each orbital can hold a maximum of two electrons with opposite spin due to the Pauli principle. So the end result is:

n=1 Shell: 1 orbital = 2 electrons

n=2 Shell: 4 orbitals= 8 electrons

n=3 Shell: 9 orbitals= 18 electrons

The number of orbitals is determined by the number of possible angular momentum states for the electrons in the atom, which is predicted by the Schrödinger Equation. So, while your pattern may seem nicer or more aesthetic, it is not what the Schrödinger Equation predicts, so it does not make more sense mathematically in the end.
 
Last edited:
Is this possible? n=6
71.5 electrons?
 
nuby said:
Is this possible? n=6
71.5 electrons?

That might be a bit difficult; splitting an electron in half is not something that you just do with a hammer and chisel...
 
Lol. nevermind
 
Last edited:
nucleus

dont forget that the nucleus also has shells and subshells.
 

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