# What is a combination of four quantum numbers that could be assigned to an electron occupying a 5p orbital?

Dec 24, 2015

$n = 5 , l = 1 , {m}_{l} = - 1 , {m}_{s} = + \frac{1}{2}$

#### Explanation:

As you know, four quantum numbers are used to describe the position and spin of an electron inside an atom. These four quantum numbers are

So, you know that you must find a valid combination of quantum numbers that can describe the position and spin of an electron located in a 5p-orbital.

In your case, the principal quantum number, $n$, which tells you on which energy level the electron resides, will be equal to $5$, since a 5p-orbital is located on the fifth energy level.

As you an see, the angular momentum quantum number, $l$, which tells you on which subshell the electron resides, can take values ranging from $0$ to $n - 1$, with

• $l = 0 \to$ describing the s-subshell
• $l = 1 \to$ describing the p-subshell
• $l = 2 \to$ describing the d-subshell**

and so on. IN your case, you need $l$ to describe the p-subshell, since a 5p-orbital is located in the 5p-subshell, i.e. the p-subshell located on the fifth energy level. Therefore, you can say that $l = 1$.

The magnetic quantum number, ${m}_{l}$, which specifies the exact orbital in which you can find the electron, can only take $3$ possible values for an electron located in the p-subshell

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

In your case, all three values for ${m}_{l}$ are possible.

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

• ${m}_{s} = + \frac{1}{2} \to$ spin-up electron
• ${m}_{s} = - \frac{1}{2} \to$ spin-down electron

Both values for ${m}_{s}$ are possible for your electron. This means that a total of six sets can describe an electron located in a 5p-orbital.

I'll give you two such sets, and leave the other four to you as practice

$n = 5 , l = 1 , {m}_{l} = - 1 , {m}_{s} = + \frac{1}{2}$

This electron is located on the fifth energy level, in the 5p-subshell, in the $5 {p}_{x}$ orbital, and has spin-up.

$n = 5 , l = 1 , {m}_{l} = + 1 , {m}_{s} = - \frac{1}{2}$

This electron is located on the fifth energy level, in the 5p-subshell, in the $5 {p}_{z}$ orbital, and has spin-down.