Quantum numbers for an electron

To describe the state of an electron in an atom, we need quantum numbers.

principal Q no.
- $n$ - goes from 1 to higher integer values.
azimuthal Q no.
- $l$ - goes from 0 to $n-1$ in integral steps - related to the magnitude of the angular momentum.
$m_{l}$
- goes from $-l$ to $+l$. It gives information about the component of angular momentum along any particular direction, which you call $z$. It is not possible in quantum mechanics to get all three components of momentum with certainty. The best you can do is to get the magnitude and one component.
spin Q no.
- $s$ for the electron which is always $\frac{1}{2}$. This is needed to reconcile the requirement of angular coservation when quatum mechanics is extended to the relativistic realm. It is the magnitude of the intrinsic angular momentum of the electron.
$m_{s}$
- just like $m_{l}$, but for the electronic spin.
Pauli's exclusion principle (1925) states that no two Fermions (electrons in this case) can have the same set of these numbers if they share the same position in space (i.e. if they are sufficiently close together).
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