Radius of isoelectronic ions

[Teemo]

Homework Statement

45. Consider the ions Li⁺, Na⁺, Be²⁺, and Mg²⁺. Which two
are closest to one another in size?
(A) Li⁺ and Na⁺
(B) Be²⁺ and Mg²⁺
(C) Be²⁺ and Li⁺
(D) Li⁺ and Mg²⁺

Homework Equations

N/A

The Attempt at a Solution

I thought it wouldn't be A, B, or D due to the pairs having different outer electron shells. I thought C would be the correct answer since they are isoelectronic and thought that the extra proton would not make too large of a difference in radius.

 

[Bystander]

Looks good. Any other questions about it?

 

[Teemo]

It's the wrong answer

 

[Bystander]

It's the wrong answer

That's embarrassing. Explanations of trends in the periodic table aren't quite as obvious as textbooks claim them to be. Just googled ionic radii, and sure enough, the "trend" is along the diagonals of the table from upper left to lower right for sizes of both the neutral atoms and the ions.

The "post hoc"^** explanation is that the extra nuclear charge does affect the radius in moving across a period approximately as much as an extra shell affects radius moving down the table through a group.

"^** "post hoc" is latin for "after the fact." Translation? I never make mistakes. It might look like what I said was in error, but really your perceptions failed to pick up the subtleties of the pearls of wisdom I cast before your swinish face, and here's the way I'm going to weasel my way out of being caught out in my own arrogant stupidity.

Bottom line? Trends in the periodic table do reflect observations made prior to the development of QM and the "Aufbau" principle used today in explaining those trends. Those trends may have motivated interest in some of the research leading to the development of QM. Take that much away from this part of your instruction in chemistry.

Do NOT feel that QM is predictive of those trends, and that you should be able to generate a QM rationalization for every observation that is made in real laboratory chemistry --- some of it can be very subtle. Some is not so subtle --- like the "diagonal" trend that we just found out is so obvious, that I've totally forgotten about it.​

 

[Borek]

To make it possible to stick to facts:

Li⁺ 1.45Å
Be²⁺ 1.05Å
Na⁺ 1.80Å
Mg²⁺ 1.50Å

(taken from http://crystalmaker.com/support/tutorials/crystalmaker/atomic-radii/index.html)

My initial guess would be C as well.

 

[Bystander]

My initial guess would be C as well.

Great minds rattle along in the same ruts.

Got thinking after this "bum steer" I gave (how many this month on "periodic trends?"). Fifty years ago, Mendeleyev was mentioned in introductions to discussions, text material, lecture material, lab material on periodic trends, but the actual trends were discussed more as consequences of quantum theory and Aufbau rather than as a body of well-established observations that contributed to some of the thinking behind the development and application of theory to atomic structure. I know that, at least in my mind, the "cart has been out in front of the horse" ever since. Just me misunderstanding the material being presented, or is it actually a bias toward theory over observation in the presentation?

 

[Teemo]

Again, sorry for being late to reply, but thanks. I guess I'll just have to memorize some of the common elements's atomic radii