Quantum Physics help/Electron trap problem

[clowe521]

Homework Statement

A rectangular corral of widths Lx = L and Ly = 1.94L contains seven electrons. What multiple of h2/8mL2 gives the energy of the ground state of this system? Assume that the electrons do not interact with one another, and do not neglect spin.

Homework Equations

Enx,ny = h^2/(8mL^2) (nx^2 + ny^2)

The Attempt at a Solution

used (nx/Lx)^2 + (ny/Ly)^2 to solve for the energy states resulting in
ground state: 1.266
1st excited: 2.063 (or 2.266?)
2nd excited: 5.063

I feel this approach is incorrect because the 1st excited state could have two possible energy states...

obviously, after finding the states, I multiplied 2 electrons by ground, 4 by 1st, and 1 by second, but the sum jumps around the answer instead of giving me a correct answer.

I'm new to the forum posting, but you guys are always a big help for me so thanks for any input ahead of time.

 

[Spinnor]

state energy
1,1 2
1,2 5
2,1 5
2,2 8

So won't the energy be 2*2 + 5*2 + 5*2 + 8*1 or 32 multiples?

 

[clowe521]

Yes, there will be 32 multiples, but that would be assuming a square electron trap...I'm not sure how to figure out the multiples based on the trap being rectangular.