Multiple electrons in an infinite square well

[ProPatto16]

Homework Statement

suppose you put 5 electrons into an infinite square well. (a) how do the electrons arrange themselves to achieve the lowest total energy? (explain with help of diagram) (b) give an expression for this energy in terms of electron mass, well width L and planks constant

The Attempt at a Solution

first off, does this well act similarly to atom in the way of electron configuration?
exclusion principle says no two electrons can have same quantum numbers, does this hold?

if so then at ground level the energy of the well is given by E_$$\infty$$=($$\pi$$²$$\hbar$$2)/2mL²

then E₁ has 2 electrons and E₂ has the last 3 electrons?

or are the first two electrons in ground level?

and then the arrangement would just be linear energy levels with the electrons?

 

[Disconnected]

Yes, the way to fill the well with the lowest possible energy is to fit as many electrons into the lowest energy states possible.

Of course the Pauli exclusion principle holds! It always holds.

 

[ProPatto16]

one more little thing... does ground level have the first two electrons? or are they in the E₁ level and ground level has none?