Question

Question #6cfda

Answer 1

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

Explanation:

For starters, you know that nitrogen's electronic configuration looks like this

`"N: " 1s^2 2s^2 2p^3`

Now, you also know that the `p` subshell contains a total of `3` orbitals. According to Hund's Rule, every orbital present in an energy subshell must be half-filled before any one of the orbitals can be completely filled.

This basically means that the first `3` electrons added to the `2p` subshell will be added to different orbitals.

https://chem.libretexts.org/Core/Physical_and_Theoretical_Chemistry/Electronic_Structure_of_Atoms_and_Molecules

Now, you're dealing with the `color(blue)(2)p` subshell, so you know that the principal quantum number, `n`, will be equal to `color(blue)(2)`.

`n = 2 ->` the second energy shell

For a `p` subshell, the angular momentum quantum number, `l`, which denotes the energy subshell in which an electron resides, is equal to `1`.

`l = 1 ->` the `p` subshell

In this case, the magnetic quantum number, `m_l`, can take three possible values, each representing an orbital located in the `p` subshell.

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

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

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

By convention, electrons added to an empty orbital are assigned spin-up, so

`m_s = +1/2`

This means that one electron located in the `2p` subshell of a neutral atom of nitrogen will have the following quantum number set

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

The other two electrons will have quantum number sets that differ only in the value of the magnetic quantum number.