- #1

- 624

- 11

You are using an out of date browser. It may not display this or other websites correctly.

You should upgrade or use an alternative browser.

You should upgrade or use an alternative browser.

- I
- Thread starter Silviu
- Start date

- #1

- 624

- 11

- #2

DrClaude

Mentor

- 7,575

- 3,922

What you have to consider in the case you describe is that you have three electrons, and you have to figure out what combinations of orbitals are possible, such that the total wave function is anti-symmetric with respect to the exchange of two electrons (Pauli principle). You will find that the lowest energy result corresponds to two electrons in the lowest energy spatial wf, with opposite spin, and one electron in a higher-energy orbital, with arbitrary spin (many solutions are possible here).

Note that I didn't say "the first and second electron" and so on, because that would not result in a wf with a definite exchange parity. The results is one where each electron can be in any of the orbitals, a linear combination of each electron being in each state. You can look up Slater determinant to figure out what these wave functions can look like.

- #3

- 33,529

- 11,946

how does the 3rd electron know the spins of the first 2?

Electrons don't have labels; you can't pick out individual electrons and say that one is the "first", one is the "second", one is the "third", and match up each label with an orbital. Electrons are indistinguishable; that means that all you can say about the state in your example is that there are two electrons in the lowest energy level and one electron in the next higher energy level. In other words, you don't have three one-electron states where one of the three has to "know" that it can't be in the lowest energy-level; you have one three-electron state that already "knows" all of the energy levels being occupied.

Share: