Calculating Energy for Exciting an Electron in a 1D Box

[kasse]

[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...

 

[Dick]

Shouldn't you maybe figure out what the solutions of the schrodinger equation in such a box are?

 

[Gokul43201]

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.)

 

[kasse]

I used the Schrödinger equation and found the energy to be 1,79*10^-17. Is it correct?

 

[Dick]

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.

 

[kasse]

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)

 

[Dick]

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.

 

[kasse]

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.

 

[Dick]

You could always flip through the wikipedia 'Particle in a box' entry for a quick intro. It's easy to find...