|Quantum Number||Quantum Name||Values|
|n||shell||1, 2, 3, 4, ... (infinity)|
|l||subshell||0, 1, 2, ... (n - 1)|
|ml||orbital||-l ... 0 ... +l|
|ms||electron spin||+1/2 or -1/2|
Each electron in an atom can have its own unique "address" or set of four quantum numbers.
Example: Consider a Beryllium atom with four electrons. Beryllium is in the second period, so possible n values are 1 and 2. Electrons are filled using the lowest value of n (or n + l), so the electrons will be placed into the n=1 shell before they enter the n=2 shell.
When n = 1, the only allowed value of l is 0; likewise, the only allowed value of ml = 0. We will place the first two electrons in a 1s orbital. Each electron can have either a "spin up" (ms = +1/2) or "spin down" (ms = -1/2) configuration.
When n = 2, allowed values of l are 0 and 1. Lowest (n + l) values are filled first; hence, a (n + l) value of (2 +0) = 2 will be filled before a (n + l) value of (2 + 1) = 3. When l = 0, the only allowed value of ml = 0. We will place the next two electrons in a 2s orbital. Each electron can have either a "spin up" (ms = +1/2) or "spin down" (ms = -1/2) configuration.
The nlx notation is used to describe the subshell and/or orbital in which the electrons are assigned in an atom or ion. The electron filling order is found by using the n + l rule or an Aufbau diagram. To avoid number duplicity, l values are assigned a letter value as follows:
|Value of l||Letter||Notes|
Example: Considering Beryllium again, we would place the first two electrons in the 1s subshell (n + l = 1 + 0 = 1), and the second two electrons in the 2s subshell (n + l = 2 + 0 = 2, so 2s is filled after 1s due to a lower (n + l) value.) The complete electron configuration for neutral Beryllium with its four electrons in the ground state would be:
Example: Considering Aluminum with its 13 electrons in the neutral ground state, we would place the electrons in successively higher subshells using the (n + l) values (or by consulting an Aufbau diagram.) The complete electron configuration for neutral Aluminum with its 13 electrons in the ground state would be: