# How does the Pauli Exclusion Principle lead to the restriction that electron with #n = 1# and #l = 0# can only take on (a linear combination of) two possible spins?

##### 1 Answer

It has to do with the quantum numbers that belong to those electrons.

- The
**principal quantum number**#n# describes the energy level, or the "shell", that the electron is in.

#n = 1, 2, 3, . . . #

- The
**angular momentum quantum number**#l# describes the energy sublevel, or "subshell", that the electron is in.

#l = 0, 1, 2, . . . , l_"max"# ,#" "" "" "" "" "" "l_"max" = n-1#

#(0, 1, 2, 3, . . . ) harr (s, p, d, f, . . . )#

- The
**magnetic quantum number**#m_l# describes the exact orbital the electron is in.

#m_l = {-l, -l+1, . . . , 0, 1, . . . , l-1, l}#

- The
**spin quantum number**#m_s# describes the electron's spin.

#m_s = pm1/2# for electrons.

And thus all four collectively describe a given *quantum state*. **Pauli's Exclusion Principle** states that no two electrons can share the same two quantum states.

Since **the electron spin must differ**, for **a given** electron in a **single** orbital.

Electrons can only be spin-up or down, **two** electrons can be in **one** orbital.

At

With only **one** orbital on **two** electrons within