Question

What are the quantum numbers for the 9th electron in flourine?

Answer 1

`n = 2, l =1, m_l = 0, m_s = -1/2`

Explanation:

You know that fluorine has an atomic number equal to `9`, which means that the `"9th"` electron in an atom of fluorine is the last one added when "constructing" the neutral atom of fluorine.

Fluorine is located in period `2` of the Periodic Table, which implies that the `"9th"` electron in fluorine is located on the second energy level.

Consequently, you can say that this electron will have a principal quantum number, `n`, which describes the energy level on which an electron is located in an atom, equal to

`n = 2`

Now, fluorine is located in group `17` of the Periodic Table, which means that fluorine is part of the `p` block.

This implies that the angular momentum quantum number, `l`, which describes the energy subshell in which the electron is located, will be equal to

`l = 1`

This is the case because you have

• `l =0 ->` describes the `s` subshell
• `l = 1 ->` describes the `p` subshell
• `l = 2 ->` describes the `d` subshell
  `vdots`

and so on. Next, for the `p` subshell, the magnetic quantum number, `m_l`, which tells you the orientation of the orbital in which the electron is located, will be equal to

`m_l = {-1, 0, +1}`

By convention, you have

• `m_l = -1 ->` describes the `p_y` orbital `->` corresponds to groups `13` and `16`
• `m_l = color(white)(-)0 ->` describes the `p_z` orbital corresponds to groups `14` and `17`
• `m_l = +1 ->` descrbes the `p_x` orbital corresponds to groups `15` and `18`

Since the `"9th"` electron corresponds to group `17`, you can say that it will have

`m_l = 0`

This electron will be added to the `2p_z` orbital, which is the `p_z` orbital located on the second energy level.

Finally, the spin quantum number, `m_s`, which tells you the spin of the electron, can take two possible values

`m_s = {+1/2, - 1/2}`

Now, the `"9th"` electron will have

`m_s = -1/2`

because, by convention, electrons added to a half-filled orbital are assigned spin-down. The `p_z` orbital is half-filled because of Pauli's Exclusion Principle, which states that all three `p` orbitals must be half-filled before any of them can be filled completely.

You can thus say that the full quantum number set that describes the `"9th"` electron in an atom of fluorine will be

`n = 2, l =1, m_l = 0, m_s = -1/2`

The electron is located on the second energy level, in the `2p` subshell, in the `2p_z` orbital, and has spin-down