Calculating Energy Levels in a 2-D Particle Box: Solving for n1 and n2

[myoplex11]

Homework Statement

For a particle in a square box of L*L dimension find how many energy levels are in the range of energy between 0 and 16 (h^2/8mL)

Homework Equations

The Attempt at a Solution

n1=1 n2 =1
n1=1 n2=2
n1=1 n2=2
n1=2 n2=2
n1=2 n2=3
i think there should be 8 total i am only getting 5

 

[buffordboy23]

[
n1=1 n2 =1
n1=1 n2=2
n1=1 n2=2
n1=2 n2=2
n1=2 n2=3
i think there should be 8 total i am only getting 5

What about

n1=1 n2=3
n1=3 n2=1
n1=3 n2=2

Also, be careful with how you are defining your energy levels. I see that you have a duplicate, but I don't think that is what you really mean.