# Width of Finite Potential Well

1. Jul 30, 2009

### JX21

For an electron in a certain rectangular well with a depth of 20.0 eV, the lowest
energy level lies 3.00 eV above the bottom of the well. Find the width of this well. Hint: Use tan theta = sin theta/cos theta.

Equation for energy levels in a rectangular well: (2E-V0)sin[(2mE)^(1/2)L/hbar] = 2(V0E-E^2)^(1/2)cos[(2mE)^(1/2)L/hbar]

I have attempted this problem multiple ways, and I have done similar problems giving me correct results. The simplified equation I typically use for this type of problem is derrived from the energy levels in a rectangular well equation. It is:

tan((L*(2mE)^(1/2))/(2*hbar)) = ((V0-E)/E)^(1/2)

where I can solve for L with everything else known. I converted the energies to J using 1 eV = 1.6E-19 J, the mass of electron = 9.11E-31 kg, and hbar = 1.05E-34 Js. The right hand of the equation = 51^(1/2)/3, and then inverse tan of that is 1.173. I then solve the problem and get L = 2.634E-10 m or 0.263 nm. The answer in the back of the book is 8.36 nm.
I have also tried using the Ti-89 solve function and Excel, but nothing gives me an answer even on the same order of magnitude. Can anyone see what I am doing wrong? Any help would be greatly appreciated.

Last edited: Jul 30, 2009