What Is the Width of a Quantum Well for a 450nm Photon Transition?

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Discussion Overview

The discussion revolves around determining the width of an infinite quantum well necessary to produce a photon with a wavelength of 450nm during an electron transition. It involves theoretical calculations and interpretations of quantum mechanics principles.

Discussion Character

  • Homework-related
  • Mathematical reasoning

Main Points Raised

  • One participant presents the problem of calculating the width of a quantum well based on a photon transition wavelength of 450nm.
  • Another participant provides the energy eigenvalue equation for an electron in a 1-D infinite square well and relates it to the energy of a photon.
  • A participant questions the correctness of the equation used, noting a discrepancy between their book's equation and the one provided.
  • One participant expresses confusion over their calculations, indicating they are obtaining unexpectedly small results compared to the expected width.
  • Another participant suggests that the difference in equations may stem from the use of h(bar) instead of h, and prompts the original poster to check their calculations again.
  • One participant confirms they arrived at a width of approximately 6.4*10^(-10) meters, but expresses frustration over not achieving the correct result in time.
  • There is a mention of potential issues with understanding the frequency aspect of the problem.

Areas of Agreement / Disagreement

Participants express varying levels of understanding and confusion regarding the calculations, with no consensus on the correct approach or final answer. Discrepancies in equations and results are noted, indicating ongoing uncertainty.

Contextual Notes

Participants reference different equations and interpretations, which may depend on specific definitions or assumptions about the quantum well model. There are unresolved mathematical steps and potential misunderstandings regarding the relationship between energy and frequency.

Who May Find This Useful

This discussion may be useful for students or individuals studying quantum mechanics, particularly those interested in quantum wells and photon transitions.

SuperCheetah
Here is a question that is giving me fits.

An electron is trapped in an infinite quantum well. If the lowest energy transition is to produce a photon of 450nm-wavelength, what should be the well's width?

Any help is appreciated. :)
 
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The energy eigenvalue equation for an electron in a 1-D infinite square well is:

E(n) = (h^2 * n^2) / (8 * m * L^2),

where L is the width of the well.

A transition of energy states requires an emission or an absorption of a photon. The energy of a photon is:

E = h * f,

where f is the frequency of the photon.

Now you've got the equations; all you have to do is plug and chug.

eNtRopY
 
Last edited by a moderator:
Nevermind got the frequency, my books equation says that there is a 2 on the bottom instead of an 8?
 
Last edited by a moderator:
Call me an idiot but I'm still not getting the correct result. The answer is 0.064nm in width, but I keep getting extremely small numbers. Is there any additional help anyone might can give without totally giving away the problem? Thanks again!
 
look closer at the 2 and 8 term, you will find that the difference is due to that h(bar)=h/(2*pi)

I´m not sure what you are doing with the equation, but you are looking for a difference, a delta E, dose that help?

Could you check you answer again, I´m getting an answer of ~ 6.4*10^(-10)?
 
That is the correct answer you got, although I still wasn't able to get it before it was due. I can't figure out what I'm doing wrong. I'll try again later I guess. Thanks for the help. I think my problem lies in the frequency.
 

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