# Question #4123c

Nov 21, 2017

$n = 3 , l = 1 , {m}_{l} = \left\{- 1 , 0 , + 1\right\} , {m}_{s} = \left\{+ \frac{1}{2} , - \frac{1}{2}\right\}$

#### Explanation:

The first thing to note here is that the coefficient added in front of the name of the subshell tells you the energy level on which the subshell is located.

In your case, the $3 p$ subshell is actually the $p$ subshell located on the third energy level. This implies that the principal quantum number, which tells you the energy level on which an electron is located inside an atom, is equal to $3$.

$n = 3$

Next, the identity of the subshell is given by the angular momentum quantum number, $l$. This quantum number can take the following values

• $l = 0 \to$ designates the $s$ subshell
• $l = 1 \to$ designates the $p$ subshell
• $l = 2 \to$ designates the $d$ subshell
$\vdots$

and so on. Since you're dealing with the $p$ subshell, you can say that you have

$l = 1$

Now, the magnetic quantum number, ${m}_{l}$, tells you the orientation of the orbital in which an electron is located.

For the $p$ subshell, you have

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

By convention, these values correspond to

• ${m}_{l} = - 1 \to$ the ${p}_{y}$ orbital
• ${m}_{l} = \textcolor{w h i t e}{+} 0 \to$ the ${p}_{z}$ orbital
• ${m}_{l} = + 1 \to$ the ${p}_{x}$ orbital

Finally, the spin quantum number, ${m}_{s}$, can take two possible values that correspond to the spin of the electron.

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

So, you can say that an electron located in the $3 p$ subshell can be described by the following quantum numbers

$n = 3 , l = 1 , {m}_{l} = \left\{- 1 , 0 , + 1\right\} , {m}_{s} = \left\{+ \frac{1}{2} , - \frac{1}{2}\right\}$

Here are three examples to go by:

$n = 3 , l = 1 , {m}_{l} = - 1 , {m}_{s} = + \frac{1}{2}$

This set describes an electron located on the third energy level, in the $3 p$ subshell, in the $3 {p}_{y}$ orbital, that has spin-up

$n = 3 , l = 1 , {m}_{l} = 0 , {m}_{s} = + \frac{1}{2}$

This set describes an electron located on the third energy level, in the $3 p$ subshell, in the $3 {p}_{z}$ orbital, that has spin-up

$n = 3 , l = 1 , {m}_{l} = 0 , {m}_{s} = - \frac{1}{2}$

This set describes an electron located on the third energy level, in the $3 p$ subshell, in the $3 {p}_{z}$ orbital, that has spin-down