What is the number of the lowest energy level that has a p sublevel?

1 Answer
Jun 23, 2017

#n = 2#.


If we seek the lowest energy level (given by the principal quantum number #n#) for which the #p# orbital sublevel exists, we look for the minimum #n# for which #l#, the angular momentum quantum number, is valid.

The principal quantum number is defined as:

#n = 1, 2, . . . #, in integer steps

and the angular momentum quantum number is defined as:

#l = 0, 1, 2, . . . , n-1#, in integer steps, where #l_max = n - 1#.

Since #p# orbitals have #l = 1#, we must have that if #l_max = n-1 = 1# is the maximum possible #l# we can achieve for a given #n#, then #bb(n = 2)# is the minimum required quantum level for #p# orbitals to exist.

Likewise...

  • #n = 1# is the minimum #n# for which #s# orbitals exist.
    (#l_max = n - 1 = 0#.)
  • #n = 3# is the minimum #n# for which #d# orbitals exist.
    (#l_max = n - 1 = 2#.)
  • #n = 4# is the minimum #n# for which #f# orbitals exist.
    (#l_max = n - 1 = 3#.)

etc.