Question

Question #66a8c

Answer 1

`"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`