Question

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

Answer 1

`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 `3d` 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 `"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 `4s` orbital.

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

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

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

`"X"^(2+) = "X"^(3+) + "e"^(-)`

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

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

Next, you have

`"X" = "X"^(2+) + 2"e"^(-)`

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

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

Therefore, you can say that a neutral atom of `"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 `"X"` must have `26` protons located inside its nucleus.

You can conclude that your unknown element is iron, `"Fe"`, which has an atomic number equal to `26`.