# Homework Help: What is the energy of the following state (quantum square)?

1. Nov 7, 2014

### spaghettibretty

1. The problem statement, all variables and given/known data

What is the energy of an STM tunneling electron in the following state? This "quantum square" model can be seen as a "particle in a 2-D box" problem.
<Refer to the picture below>
The protrusions are Fe atoms and the surface is Cu(111).
Given that the radius of an Fe atom is 126 pm (1.26e-10 m), I've calculated that the shorter side, Lx, equals 2.02e-10 m. Likewise, the longer side, Ly equals 2.77e-10 m.

Lx = 2.02e-10 m
Ly = 2.77e-10 m
h = Planck's constant = 6.626e-34 J*s
m = effective mass of an electron in this scenario = 0.38me = 0.38 * 9.109e-31 kg = 3.461e-31 kg

2. Relevant equations

E = n^2 * h^2 / (8*m*L^2)
Ex, y = nx^2 * h^2 / (8 * m * Lx^2) + ny^2 * h^2 / (8 * m * Ly^2)

3. The attempt at a solution

All I need to know are the constants, nx and ny, the rest of the problem would just be a plug and chug. Although, I don't think the number of Fe atoms represent the n constants. I believe that the number of nodes + 1 would give me the values I need, but I'm not quite sure what in this picture represents the nodes. Do the black dots in the square represent the nodes? Or do they represent the actual n values? If they represented the n values, would nx = 3 and would ny = 4?

2. Nov 12, 2014