Some rules that are useful for the aufbau technique

The following are some rules that are useful for determining haw to assign quantum numbers to electrons in atoms according to the aufbau (building upon) technique.  (The aufbau technique assume that the energy levels of atoms are the same as the levels found in the hydrogen atom.)  These rule will aid in the selection of quantum numbers for the ground state (lowest energy state) of an atom.


 Rule
 Description
1)
 Pauli exclusion principle*
 No two electrons may have the same set of quantum numbers
2)
 selecting n
 (For any particular l) the lower the value of n, the lower the energy.
3)
 selecting l
 (For any particular n) the lower the value of l the lower the energy.
4)
 selecting ml
 In filling ml, initially they all have the same energy value.
5)
 selecting ms
 Initially ms either + or − have the same energy
6)
 Hund's rule
 If either ml or m s could be changed to the next electron,  ml changes before ms.

There are some additional rules that will be obvious from the periodic chart.

Regardless of whether the atom is in the ground state or not, the electrons must obey the following selection rules*

The addition of electrons in this scheme must always follow the selection rules:
1)
 For the principal quantum number, n:
n = 1 or 2 or 3 or 4 ....  i.e. an even positive integer.
2)
 For the subsidiary quantum number, l:
 0 =< l =<  n-1
3)
 For the magnetic quantum number, ml :
  -l =< ml =< +l
4)
For the spin quantum number, ms :
  ms  = +1/2 or -1/2

* electrons must also always obey the Pauli exclusion principle.

Click here to see the electron quantum numbers of the ground states for the first 10 atoms.