# An unknown element "X" has electron configuration ["Ar"]3d^5 and a charge of 3+. What is the atomic number of "X"?

Oct 1, 2017

$26$

#### Explanation:

For starters, you know that your element is located in period $4$ of the Periodic Table because all the transition metals that have $3 d$ configurations are located in period $4$ of the Periodic Table.

This means that you can write the noble-gas shorthand configuration for this unknown element, let's say $\text{X}$, like this

"X"^(3+): ["Ar"] 3d^5

Now, the trick here is to realize that when a transition metal located in period $4$ is losing electrons, the first two electrons that are lost are coming from the $4 s$ orbital.

In other words, when the $4 s$ orbital is occupied, it is actually higher in energy than the $3 d$ orbitals. Keep in mind that when the $4 s$ orbital is empty, it is actually lower in energy than the $3 d$ orbitals!

So when $\text{X}$ is losing the first two electrons, they are being taken from the $4 s$ orbital. Consequently, you can say that when the element is losing the third electron, this electron will come from the $3 d$ orbitals.

You can thus backtrack and add electrons to the $3 +$ cations to form the neutral atom.

${\text{X"^(2+) = "X"^(3+) + "e}}^{-}$

This means that you have--remember, the third electron was removed from the $3 d$ orbitals, so it must be added back to the $3 d$ orbitals!

"X"^(2+): ["Ar"] 3d^6

Next, you have

${\text{X" = "X"^(2+) + 2"e}}^{-}$

This means that you have--the first two electrons were removed from the $4 s$ orbital, so they must be added back to the $4 s$ orbital!

"X": ["Ar"]3d^6 4s^2

Therefore, you can say that a neutral atom of $\text{X}$ has a total of

overbrace("18 e"^(-))^(color(blue)("the same as neutral atom of Ar")) + overbrace("6 e"^(-))^(color(blue)("in the 3d orbitals")) + overbrace("2 e"^(-))^(color(blue)("in the 4s orbitals")) = "26 e"^(-)

This implies that a neutral atom of $\text{X}$ must have $26$ protons located inside its nucleus.

You can conclude that your unknown element is iron, $\text{Fe}$, which has an atomic number equal to $26$.