How many orbitals are in the 3d subshell?

1 Answer
Nov 6, 2015

Answer:

Five.

Explanation:

The important thing to realize here is that there's nothing special about the 3d-subshell in terms of the number of orbitals it contains.

The d-subshell contains five orbitals regardless of the energy level on which the subshell is located - as long as #n>=3#.

Each subshell is characterized by a distinct value of the angular momentum quantum number, #l#. The number of orbitals each subshell can hold is determined by the magnetic quantum number, #m_l#.

The relationshop between the principal quantum number, #n#, the angular momentum quantum number, #l#, and the magnetic quantum number, #m_l#, can be described like this

#l = 0, 1, 2, ..., n-1#

and

#m_l = -l, -(l-1), ..., -1, 0, 1, ..., (l-1), l#

Now, the d-subshell is described by #l=2#. This mens that any d-subshell you'll ever run into will have a total of five d-orbitals described by

#m_l = {-2; -1; 0; 1; 2}#

Therefore, the 3d-subshell will contain a total of five 3d-orbitals.

Likewise, the 4d-subshell will contain a total of five 4d-orbitals, the 5d-subshell will contain a total of five 5d-orbitals, and so on.