Understanding Electron Shells: Defined by Principal Quantum Number

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Discussion Overview

The discussion centers on defining electron shells in the context of quantum mechanics, specifically focusing on the principal quantum number and its implications for electron energy levels and spatial distribution. Participants explore the characteristics of electron shells, their distances from the nucleus, and the differences between various types of orbitals.

Discussion Character

  • Conceptual clarification
  • Debate/contested
  • Technical explanation

Main Points Raised

  • Some participants propose that electron shells are defined by the principal quantum number, which indicates the energy level of an electron.
  • There is a question about whether electrons in the same shell are all roughly the same distance from the nucleus, leading to a discussion about the geometries of different orbitals.
  • One participant argues that while s-orbitals and p-orbitals can be compared, their distances from the nucleus can vary significantly, especially as the principal quantum number increases.
  • A later reply clarifies that the radial density distribution of orbitals can lead to situations where a 2s orbital may have its maximum farther out than a 2p orbital, while also noting that 3d orbitals can be more diffuse than 3p orbitals.

Areas of Agreement / Disagreement

Participants express differing views on the relationship between orbital types and their distances from the nucleus, indicating that the discussion remains unresolved regarding the specifics of electron positioning within shells.

Contextual Notes

There are limitations in the discussion regarding the assumptions made about orbital geometries and energy levels, as well as the dependence on definitions of terms like "distance" and "energy level." The nuances of radial density distributions are also noted but not fully explored.

ldv1452
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What would be the best way to define electron shell? I know that it is identified by the principal quantum number, but not sure how to clearly define it.
 
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ldv1452 said:
What would be the best way to define electron shell? I know that it is identified by the principal quantum number, but not sure how to clearly define it.

It essentially represents the energy level of an electron IIRC.

CS
 
stewartcs said:
It essentially represents the energy level of an electron IIRC.

CS

Are electrons in the same shell all roughly the same distance from the nucleus then?
 
ldv1452 said:
Are electrons in the same shell all roughly the same distance from the nucleus then?

Not really; because the different orbitals have such quite different geometries. If you compare s-orbitals with s-orbitals or p-orbitals with p-orbitals their distance from the nucleus increases as the shell does.
 
alxm said:
Not really; because the different orbitals have such quite different geometries. If you compare s-orbitals with s-orbitals or p-orbitals with p-orbitals their distance from the nucleus increases as the shell does.

So is that saying that if you compare s-orbitals with p-orbitals that may not hold true? For example, could you have an electron in a p-orbital of the 2nd shell with a higher energy level and/or further distance from the nucleus than that of an electron in the s-orbital of the 3rd shell?
 
ldv1452 said:
So is that saying that if you compare s-orbitals with p-orbitals that may not hold true? For example, could you have an electron in a p-orbital of the 2nd shell with a higher energy level and/or further distance from the nucleus than that of an electron in the s-orbital of the 3rd shell?

No, but for instance, if one looks at the radial density distribution, the 2s orbital has its maximum farther out than the 2p orbital. 3d is farther in than 3p, but on the other hand, 3d is a lot more diffuse. (1s, 2p, 3d, 4f have no radial nodes and are therefore more diffuse).
 

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