Quantum Mechanics Question 1-D Well

[painedcompute]

Homework Statement

Light of various wavelengths is shined on a collection of "quantum wires" all of the same length. Each 'wire' consists of an electron trapped in a carbon nanotube, which we approximate as a 1-D infinite potential well of a width equal to the length of the wire.

It is observed that the longest wavelength that is absorbed by the collection of wires (corresponding to an electronic excitation in each wire), is 0.44 mm. What is the length of each wire?

Homework Equations

En = (h^2/(8mL^2))n^2
E = hc/lamda

The Attempt at a Solution

Ok, so I actually know the answer to this question. It is 20 nanometers. I can't figure out what I'm doing wrong, though. Here is what I did:

First calculate the energy being absorbed:

E = hc/lamda = 1240 / (.44*10^6) = .0028182

Then I use that to find L, the length of the wire (width of the potential well):

E1 = (h^2/(8mL^2))1^2
L^2 = (1.505/(4*.0028182))
L = (1.505/(4*.0028182))^.5 = 11.555 nm

The answer should be 20 nm, where and how did I go wrong?

 

[painedcompute]

Did I post this in the wrong forum? I see a lot of quantum mechanics in the advanced physics forum.

 

[nlightner]

Your approach is correct, but there is a small error in your calculation. The correct value for L^2 is 1.5048/(4*0.0028182), which gives L = 20.000 nm. It seems like you accidentally used 1.505 instead of 1.5048 in your calculation. Other than that, your logic and equations are correct.