Trend of First Ionization Energy in the Periodic Table

[Itskitty]

Why do metals generally have lower ionization energies than non-metals?

I mean, doesn't ionization energy depend on the atomic radius?

And the atomic radius is in turn dependent on the shell and the protons.

According to these factors, the atomic radius of Sodium should be smaller than
lower period non-metals such as Bromine.

Smaller atomic radius means that the proton can attract valence electrons much more strongly.

Therefore, Sodium's IE must be higher than that of Bromine.

But it's not the case. Why?

 

[Itskitty]

ok I'm wrong here about the trend

so we actually have to look at the trend in atomic radius of metals and non-metals separately.

Why?

 

[Itskitty]

a clearer question is:
Why doesn't non-metals in the (n+1)th shell
have greater radius than metals in the nth shell
although it is the case for metals in the n+1 th shell?

 

[Borek]

doesn't ionization energy depend on the atomic radius?

No, it doesn't. There is no such dependency, so all your thinking is based on a wrong assumption.

--

 

[Itskitty]

No?
But i thought tht smaller radius means tht the nucleus has a tighter hold on the valence electron
ths increasing the ionization energy?

Would u please correct my misunderstanding here?

 

[Borek]

To some extent you are right, but this approach is way too simplified to give correct results. It would work for equivalent electrons. But electrons are not equivalent, they occupy orbitals - and amount of energy needed to remove electron depends on the energy of orbital the electron is on. This dominates the situation.

 

[Itskitty]

I don't see it in my chemistry book (chang's general chemistry) could you tell me what topic of chemistry will help me to understand this?
Thanks so much!

 

[Borek]

Any intro to quantum chemistry and quantum numbers will do. Don't have to be mathematically heavy.

--

 

[alxm]

Borek: Well the first ionization potential does actually have one radius-related property, which is that there's a (not very well-)known relation to the asymptotic behavior of the electronic wave function (or density). (E.g. Katriel and Davidson, PNAS, v77, no 8, p4403)

I have to say I think those introductory/general chem textbooks fret far too much over atomic radii. As you said, there are no simple rules - and I'd add that it's not a terribly useful property. From a theoretical POV you'd be better learning more about orbitals, and from a practical/structural POV, one would be better off learning the lengths of common bonds.

So don't fret Itskitty, there's no absolute definition of what an atomic radius even is, much less any absolute rules on how it corresponds to other properties. I still find myself gaining new insights all the time, after spending years studying the stuff!