Calculating Energy for Exciting an Electron in a 1D Box

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Homework Help Overview

The discussion revolves around calculating the energy required to excite an electron in a one-dimensional box with infinite potential walls. The specific parameters include a box length of 1.0 x 10^-10 m and the focus is on determining the energy difference between the ground state and the first excited state.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the relevance of the Schrödinger equation for the problem and the derivation of energy eigenvalues. Questions arise regarding the methods used to calculate energy and the interpretation of results, including the need to clarify the formula for energy differences.

Discussion Status

Some participants have provided guidance on using the Schrödinger equation and checking the calculations for energy levels. There is an ongoing exploration of different methods and interpretations, with no explicit consensus reached on the correctness of the calculations presented.

Contextual Notes

Participants note that this is part of an introductory course in nanotechnology, with no textbook provided, which may influence the depth of understanding and resources available for solving the problem.

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[SOLVED] Exciting an electron

An electron is in a 1-dimensional box with infinite potential on both sides. The length of the box is 1,0*10^-10 m. How much energy does it take to excite the electron to the first excited level?

Hm, I've got no idea how to solve this one...
 
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Shouldn't you maybe figure out what the solutions of the Schrödinger equation in such a box are?
 
kasse said:
An electron is in a 1-dimensional box with infinite potential on both sides. The length of the box is 1,0*10^-10 m. How much energy does it take to excite the electron to the first excited level?

Hm, I've got no idea how to solve this one...
Have you looked at what your textbook has to say about this? What text are you using? Is this a calculus-based course?

(Aside: Dick, I've seen pre-calculus physics courses where the 1D infinite well is introduced without any reference to the SE. The derivation of energy eigenvalues involves using the de Broglie relation on allowed wavelengths for standing waves in the well.)
 
Last edited:
I used the Schrödinger equation and found the energy to be 1,79*10^-17. Is it correct?
 
Is that in joules? What sort of an equation did you finally put numbers into? No matter what method you use (thanks, Gokul), you should find that there is more than one possible energy for the particle in the box to have. Do you have a formula for these possible energies? The problem is asking about the energy difference between two of them.
 
Yes, in Joules.

I used the eq

Delta(E)=(h'*(pi)^2*(n+1)^2)/2mL^2 - (h'*(pi)^2*n^2)/2mL^2

where h' = h/(2*pi)
 
Ok, then put n=1, right? So you get the difference between the n=2 state and the n=1 state. It looks fine to me. You really meant h'^2 in the equation, your answer is right so I'm guessing you did.
 
yeah, h'^2.

This is just homework as a part of an intro course in nanotechnology. There's no book, only lectures. I think I should try to find some info on my own to improve my understanding.
 
You could always flip through the wikipedia 'Particle in a box' entry for a quick intro. It's easy to find...
 

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