I’m in my first year of teaching high school chem, and a girl caught me at the end of the period with a question I couldn’t answer:
Why is the ionic radius of +3 Beryllium larger than that of +2 Boron? There is the same number of electrons, and Be has one more proton to attract the electrons in tighter.
Thanks.
First off, I take it you actually meant Be[sup]2+[/sup] and B[sup]3+[/sup] (which have the same number of electrons), and that boron has one more proton in its nucleus than beryllium.
This mix-up may be the source of your confusion, because your question as stated does not make sense.
In any event, Be[sup]2+[/sup] is indeed larger than B[sup]3+[/sup], for exactly the reason stated in your question. Both ions have the same number of electrons, and boron has one additional proton, which pulls its electrons in tighter.
For experimental verification, I came across a value of 31 pm for the size of Be[sup]2+[/sup], and 20 pm for the size of B[sup]3+[/sup] in a literature search.
robby: Those atomic radii are the Pauling ionic radii, which are an older measurement that is ‘wrong’ for a few reasons (they’re based on the distance between ions in ionic crystals rather than on actual electron density). The Pauling radii are still practically useful, and understanding the more modern, more accurate Shannon radii requires knowledge of coordination geometry, which is beyond the level of high-school chemistry students.
Be[sup]3+[/sup] is not encountered because the third ionization potential for beryllium is much higher (14848 kJ/mol) than the second (1757 kJ/mol). Boron(I) compounds do exist and boron(II) also exists, as in B[sub]2[/sub]F[sub]4[/sub].
I agree that the reason is simply because B[sup]3+[/sup] has the same electron configuration (1s[sup]2[/sup]) as Be[sup]2+[/sup] but B[sup]3+[/sup] has an extra proton. Increased nuclear charge leads to a smaller radius for the 1s orbital (and the others). Proving this mathematically would be rather difficult for me and might well cause your student to abandon any interest in math or science she might have. =) But the explanation that the extra proton pulls the electrons closer to the nucleus is entirely adequate.
I can’t believe I screwed that up. Of course it’s Boron that might go +3. It’s right there in the book.
But the point is that the book shows B +3 as larger than Be +2. That’s my point. Is there anything conceptually that I might relay that would satisfy their curiosity?
The numbers I provided are indeed the Pauling ionic radii, which are based on the distance between nuclei in ionic crystals using x-ray diffraction, IIRC.
I believe the Pauling ionic radii, even if not completely accurate for a lone ion, should allow for a comparison to be made between the two ions.
It sounds like your textbook may be incorrect. This is not entirely uncommon, and it presents a good learning opportunity for your students.
This website has a wealth of reference info:
http://www.webelements.com/