Question

How to assign $4$ quantum numbers to $2$ electrons in $3p$ orbitals?

Answer 1

As we know that there are total four quantum numbers namely principal quantum number, azimuthal quantum number, magnetic quantum number and spin quantum number and we also know that these quantum numbers can tell us about the location and spin of an electron present inside an atom.

Complete step-by-step answer:
As we know that the principal quantum number tells us about the energy levels of shells of an atom where the electron resides. It is represented as $'n'$ and the shells are represented as alphabets K, L, M, N and so on. And for $3p$ orbital, the value of principal quantum number is $n = 3$ i.e. the electron is present in the third energy level.

Next we have, azimuthal quantum number which basically informs us about the subshell of an atom where the electron is present. It is represented by $'l'$ and the subshells are represented by p, d, f and so on. And we have $3p$ orbital where for a p-orbital, the value of azimuthal quantum number is assigned as $l = 1$.

Now, we have next quantum number which is our magnetic quantum number which is represented by $'m'$ and for a p-subshell we know that the value of this quantum number can be given as the $- l$ to $+ l$ i.e. $m = - 1,0, + 1$.

Finally, we have our spin quantum number which tells us about the spin of an electron and it can only take two possible values either a positive half or a negative half and it is normally represented as $'{m_s}'$.

Therefore, we got the set of all the four quantum numbers that is the two electrons in $3p$ orbital can either have the set as given below:
$n = 3 \\\ l = 1 \\\ m = - 1 \\\ {m_s} = + \dfrac{1}{2} \\\$
Where, one electron is clearly seen located in the third energy level or shell in the $3p$ subshell inside the $3{p_x}$ orbital having an upper spin. Or it can have a set of all four quantum number as:
$n = 3 \\\ l = 11 \\\ m = - 1 \\\ {m_s} = - \dfrac{1}{2} \\\$
That is, this electron is present in the third shell in a $3p$ subshell inside a $3{p_x}$ orbital possessing a downward spin.

Note: The above given set is described when the electron is located in same orbital that is $3{p_x}$ orbital, similarly we can have these two electrons in different orbitals which are $3{p_y}$ and $3{p_z}$ and only the spin quantum number will different in these two orbital and all the other numbers will be same.