Question #8e71b

Sep 19, 2017

$\textcolor{red}{2} {\textcolor{b l u e}{p}}_{\textcolor{g r e e n}{z}} \to n = \textcolor{red}{2} , l = \textcolor{b l u e}{1} , {m}_{l} = \textcolor{g r e e n}{0}$

Explanation:

For starters, you should know that the coefficient added to the name of the orbital tells you the energy shell in which the orbital, and consequently, the electron(s) it holds, is located.

In other words, the coefficient added to the name of the orbital tells you the value of the principal quantum number, $n$.

$n = 2 \to$ the ${p}_{z}$ orbital is located in the second energy shell

Now, you know that you're dealing with a specific orbital because you have a subscript added to the name of the energy subshell.

In your case, you have $z$ as a subscript, which means that you're dealing with one of the three orbitals located in the $2 p$ subshell. We denote the energy subshell in which an orbital is located by using the angular momentum quantum number, $l$.

For the $p$ subshell, you have

$l = 1 \to$ the ${p}_{z}$ orbital is located in the $2 p$ subshell

Like I said, the name of the orbital is given by the subscript added to the name of the subshell. This is denoted by the magnetic quantum number, ${m}_{l}$, which, for the $p$ subshell, can take the following values

${m}_{l} = \left\{- 1 , 0 , + 1\right\}$

By convention, the $z$ subscript, which denotes the ${p}_{z}$ orbital, is given by ${m}_{l} = 0$.

${m}_{l} = 0 \to$ the ${p}_{z}$ orbital

Finally, the spin quantum number, ${m}_{s}$, can take two possible values

${m}_{s} = \left\{- \frac{1}{2} , + \frac{1}{2}\right\}$

This means that a $2 {p}_{z}$ orbital can be represented by $2$ quantum number sets.

$n = 2 , l = 1 , {m}_{l} = 0 , {m}_{s} = + \frac{1}{2}$

This describes an electron located in the second energy shell, in the $2 p$ subshell, in the $2 {p}_{z}$ orbital, that has spin-up

$n = 2 , l = 1 , {m}_{l} = 0 , {m}_{s} = - \frac{1}{2}$

This describes an electron located in the second energy shell, in the $2 p$ subshell, in the $2 {p}_{z}$ orbital, that has spin-down