What is the box in particle in a box?

  • Context: High School 
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Discussion Overview

The discussion revolves around the concept of the "box" in the particle in a box model, particularly in relation to its analogy in atomic systems. Participants explore the implications of this model for understanding quantization of energy and its relation to wavelengths, with a focus on its applicability to high school chemistry education.

Discussion Character

  • Exploratory, Conceptual clarification, Debate/contested

Main Points Raised

  • One participant expresses uncertainty about whether the "box" should be considered as an energy level or an orbital, indicating a need for clarification on its meaning in the context of quantum mechanics.
  • Another participant questions the analogy of the box in relation to an atom of hydrogen, acknowledging the model's limitations.
  • A third participant describes the one-dimensional box as a potential with infinite walls, clarifying that it is not an energy level and that energies and orbitals are derived from solving the Schrödinger equation for this potential.
  • Another participant emphasizes that the box is a simplified model that serves as a Gedankenexperiment, noting its limitations in accurately representing atomic systems due to the absence of sharp boundaries.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the interpretation of the box, with multiple competing views regarding its analogy to atomic structures and its overall applicability in real physical systems.

Contextual Notes

Some limitations are noted, such as the model's dependence on idealized assumptions and its inadequacy in representing the complexities of atomic systems.

mishima
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Hi, I am trying to demonstrate the relation between quantization of energy and wavelengths in a confined box for high school chemistry students. I am following an approach found in Atkins' "Chemical Principles". Anyways, its quite understandable, but I get the feeling maybe the box isn't actually what I think it is. I've been thinking of the box as the energy level (shell). But is it actually the orbital? Or something else entirely? Thanks.
 
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Is this a bad question? I understand its just a model, but what is the box analogous to for say, an atom of hydrogen?
 
A one dimensional box is a potential V(x) which is infinite for e.g. x<0, zero for x>=0 and x<=L and again infinite for x>L.
It is not an energy level. The energies and orbitals arise when you solve the Schroedinger equation for a particle moving in that potential.
 
The box is really just a box: a volume with walls which are impenetrable for the particle. Although this is a valid approximation for some real physical systems, it is primarily a Gedankenexperiment which is easy to calculate and illustrates the behaviour of quantum mechanical systems. Especially, it is a quite bad model for atoms because they have no sharp boundary like the box.
 

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