Question #6cfda

1 Answer
Dec 5, 2017

Answer:

#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.