Pauli exclusion principle question

[drullanorull]

I have a question in my book where five electrons are placed in a infinite square well and I am supposed to calculate the lowest energies. My problem is with the electron configuration. I think that the first two shall be placed in n=1 and then the rest shall be placed in n=2. This since l=0,1 and m=-1,0,1 (plus the spin). However my book gives me a different solution. Two in n=1, two in n=2 and one in n=3, due to Pauli exclusion. But three electrons can have different quantum numbers in n=2. So why shall one of the electroons be placed in n=3?

 

[malawi_glenn]

Is the well spherical symmetric? No.

In the infinite square well, your quantum numbers are only n and m_s, you don't have L since it isn't spherical symmetric - hence angular momentum is not a good quantun number here.

So for each n, you can put 2 number of electrons due to 2 different m_s values.

So L only plays a role if your potential has spherical symmetry - in the atom for example - the nuclei is generating a spherical symmetric potential - and here L quantum number becomes important.

 

[drullanorull]

of course! thanks a lot