# Question #66a8c

##### 1 Answer

#### Explanation:

The principal quantum number, **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 = {0, 1, ..., n-1}#

In your case, the third energy shell contains **subshells**, since

#l = {0, 1, 2}#

The number of orbitals is given by the magnetic quantum number,

#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 **orbitals**, each given by a specific combination of

Keep in mind that the number of orbitals that can be found on a given *energy level*

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

For

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