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

[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. :)

 

[eNtRopY]

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

 

[SuperCheetah]

Nevermind got the frequency, my books equation says that there is a 2 on the bottom instead of an 8?

 

[SuperCheetah]

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!

 

[Custodian]

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)?

 

[SuperCheetah]

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.