# Question #ec78b

Jan 30, 2017

Magnesium.

#### Explanation:

As you know, we can use four quantum numbers to describe the location and spin of an electron inside an atom.

Now, you know that the outermost electron in an unknown atom can be described using the quantum number set

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

The principal quantum number, $n$, describes the energy level on which the electron resides. In this case, the outermost electron is located on the third energy level, which corresponds to the third period of the Periodic Table of Elements.

In other words, elements that are located in the third period of the Periodic Table has their outermost electron(s) located on the third energy level.

The angular momentum quantum number, $l$, tells you the subshell in which you can find the electron. You can have

• $l = 0 \to$ the s subshell
• $l = 1 \to$ the p subshell
• $l = 2 \to$ the d subshell
• $l = 3 \to$ the f subshell

and so on. In your case, the outermost electron is located in the $s$ subshell.

The magnetic quantum number, ${m}_{l}$, tells you the orientation of the orbital that holds the electron. The $s$ subshell can hold a single orbital, the $s$ orbital. The $s$ orbital corresponds to group 1 and group 2 of the Periodic Table of Elements.

Finally, the spin quantum number, ${m}_{s}$, tells you the spin of the electron. In your case, the electron is said to have spin-down, since ${m}_{s} = - \frac{1}{2}$.

Now, the $s$ orbital, much like any other orbital, can hold a maximum of $2$ electrons, one having spin-up and one having spin-down.

By convention, we tend to use ${m}_{s} = + \frac{1}{2}$ for the first electron that occupies the orbital and ${m}_{s} = - \frac{1}{2}$ for the second electron that occupies the orbital.

• ${m}_{2} = + \frac{1}{2} \to$ the element is located in group 1
• ${m}_{s} = - \frac{1}{2} \to$ the element is located in group 2

This means that your atom is magnesium, $\text{Mg}$, which is located in period 3, group 2 of the Periodic Table, in the $s$ block.