Question

What is the third energy level of a an electron in a 3 D cube of side length 1 nanometer? What is the degeneracy at this energy?

Answer 1

For 3D cube; L_x=L_y=L_z

n_x , ny, n_z are quantum states of the electron

For 1st Energy state; a=3 (1,1,1)

For 2nd Energy state; a=6 (2,1,1) , (1,1,2), (1,2,1)

For 3rd Enery level; a=9 (2,2,1) , (2,1,2), (1,2,2)

.... and so on

So, for 3rd energy level

Total Energy:

which is the required answer

Putting values of h =6.626*10^-34  m=9.1*10^-31 L=1*10^-9

Now , for 3rd energy level there are 3 quantum state for the same energy and so 3 different wave function

So, degenerecy is the number of wavefunction that is formed in a particular state. Thus, degenrecy of the function is 3.