Evaluate QM Potential Well Proposal for Low-n Transitions

[bobcat817]

Homework Statement

An experimental physicist submits a proposal to a granting agency requesting support to construct an infinite potential well analogous to the one shown in Figure 3.5 (an electron trapped in a one dimensional box made of electrodes and grids in an evacuated tube). Specifically, the proposal is to build a well with L = 1mm, inject some electrons into it, and then measure the wavelength of photons emitted during low-n transitions via optical spectroscopy. As an expert on quantum mechanics, you are asked to evaluate the proposal. What is your recommendation?

Homework Equations

E = $$\frac{\pi^2\hbar^2}{2 m L^2}n^2$$

$$\lambda$$ = $$\frac{h c }{E}$$

The Attempt at a Solution

Questions: Can electrons transition without a nucleus? Is it responding to some nucleus outside of the well? Does it have nothing to do with nuclei at all? What exactly are low-n transitions?

I'm very confused, so any direction would be appreciated. I know that the proposal should be refused, but I don't know why. By playing around with the equations above, I though perhaps that the wavelength wasn't in the visual spectrum, but I'm not sure that combining the two equations even makes sense.

 

[olgranpappy]

you can take "low-n transitions" to mean n=1 or 2 or so. That is, plug in n=1 or 2 or whatever to the 'E' formula and find E. Then plug that E into the '$\lambda$ formula and find $\lambda$. Compare the wavelength you find to the wavelength of visible light.

 

[bobcat817]

Thank you very much. That's what I did initially, but I wasn't sure if that was the right method.