## What is the equation: En= (n^2*h^2)/(8*m*L^2) used for? [ENDORSED]

$E_{n}=\frac{h^{2}n^{2}}{8mL^{2}}$

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### What is the equation: En= (n^2*h^2)/(8*m*L^2) used for?

Question: What is the equation: En= (n^2*h^2)/(8*m*L^2) used for?

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### Re: What is the equation: En= (n^2*h^2)/(8*m*L^2) used for?  [ENDORSED]

Answer: This gives the energy of a particle in a model system. The model system is often called "particle in a box", and it involves an imaginary box of length L, with an energetic particle like an electron inside, of mass m. We use this model system to try to understand how an electron would behave it were to be like a standing wave, because the particle in the box is given standing wave properties with its own simple wave equation.

Se-Young Lee
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### Re: What is the equation: En= (n^2*h^2)/(8*m*L^2) used for?

I noticed that the energy of the particle approaches infinity as the limit of the length of the box approaches zero-- would this imply that the size of the 'box' affects the energy of the particle?

704320688
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### Re: What is the equation: En= (n^2*h^2)/(8*m*L^2) used for?

You asked: I noticed that the energy of the particle approaches infinity as the limit of the length of the box approaches zero-- would this imply that the size of the 'box' affects the energy of the particle?

I believe that the size of the box and the energy of the particle are directly related as the n-level of every box will vary with whatever is in it. This box models one of the simplest atom systems, hydrogen, which has only one electron. If you were to go just one across on the periodic table to Helium, you'd notice that the walls of the box are much larger and the electrons (and energy levels) are held more closely together (due to an increase in the number of protons).

Magdalena Palavecino 1A
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### Re: What is the equation: En= (n^2*h^2)/(8*m*L^2) used for?

I am having trouble understanding the math questions that we could be asked in the test that could have to do with this concept. I understand the idea, but we have never seen it in class. Will we need to use it in the test?

Dylan Mai 1D
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### Re: What is the equation: En= (n^2*h^2)/(8*m*L^2) used for?

Does anyone have an answer for the question above yet? I also do not remember seeing this formula in lecture