Question #66a8c

1 Answer
Jan 28, 2017

Answer:

#"9 orbitals"#

Explanation:

The principal quantum number, #n#, corresponds to the energy shell that holds an electron in an atom. Each energy shell contains a specific number of subshells, which in turn contain a specific number of orbitals.

The number of shells is given by the angular momentum quantum number, #l#, which can take the following values

#l = {0, 1, ..., n-1}#

In your case, the third energy shell contains #3# subshells, since

#l = {0, 1, 2}#

The number of orbitals is given by the magnetic quantum number, #m_l#, which can take the following values

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

In your case, you have

  • #l = 0 implies m_l = 0#
  • #l=1 implies m_l = {-1, 0, 1}#
  • #l=2 implies m_l = {-2, -1, 0, 1, 2}#

This means that the third energy level holds #9# orbitals, each given by a specific combination of #l# and of #m_l#.

Keep in mind that the number of orbitals that can be found on a given energy level #n# is equal to

#color(blue)(ul(color(black)("no. of orbitals" = n^2)))#

For #n=3#, you will once again find

#"no. of orbitals" = 3^2 = 9#