# Question #27e4d

Jun 10, 2016

This is actually hard to do completely without actual data.

INITIAL GUESS

My initial ordering would be based on charge (smallest to largest):

1. ${\text{Al}}^{3 +}$
2. ${\text{Mg}}^{2 +}$
3. ${\text{Na}}^{+}$
4. $\text{Ne}$
5. ${\text{F}}^{-}$
6. ${\text{O}}^{2 -}$
7. ${\text{O}}^{3 -}$

since a larger positive charge gives a larger effective nuclear charge relative to an element on the same period with a smaller positive charge, and thus a smaller ionic radius.

But we are looking way across the periodic table, and the period trend and group trend overlap.

PERIOD/GROUP TREND CONFLICTS

Recall that the atomic radius resets to be bigger due to the addition of a new quantum level $n$, so $\text{Ne}$ is smaller than ${\text{Na}}^{0}$. However, that doesn't tell us everything we need to know.

How much smaller does $\text{Mg}$ get upon two ionizations, and $\text{Na}$ get after one ionization? That's what I don't know. We can still say that ${r}_{{\text{Na"^(+)) > r_("Mg}}^{2 +}}$, but...

• $\text{53 pm}$ (ionic radius)
• $\text{72 pm}$ (ionic radius)
• $\text{102 pm}$ (ionic radius)
• $\text{69 pm}$ (covalent radius)
• $\text{133 pm}$ (ionic radius)
• $\text{140 pm}$ (ionic radius)
• $> \text{140 pm}$ (ionic radius)

respectively, for the species listed at the top.

So I would have misplaced $\text{Ne}$. Apparently, ${\text{Mg}}^{2 +}$ is very slightly larger than $\text{Ne}$, by virtue of its added quantum level.

(And I could also be wrong if the atomic radii I referenced were poorly calculated or poorly determined as well, because $\text{3 pm}$ is not a large margin of error.)

The "real" order, at least based on the data I referenced, would be (from smallest to largest):

1. ${\text{Al}}^{3 +}$, ${r}_{\text{ionic" = "53 pm}}$
2. $\text{Ne}$, ${r}_{\text{covalent" = "69 pm}}$
3. ${\text{Mg}}^{2 +}$, ${r}_{\text{ionic" = "72 pm}}$
4. ${\text{Na}}^{+}$, ${r}_{\text{ionic" = "102 pm}}$
5. ${\text{F}}^{-}$, ${r}_{\text{ionic" = "133 pm}}$
6. ${\text{O}}^{2 -}$, ${r}_{\text{ionic" = "140 pm}}$
7. ${\text{O}}^{3 -}$, ${r}_{\text{ionic" > "140 pm}}$