[Fobbit]

I have just noticed that the IONIC radius of Li+ is 76 pm where as the ATOMIC radius of He is only 31 pm. I would have suspected that the former would be equal to He's radius given that both have only the two 1s electrons in their cloud. In fact, one could hypothesize that Li+'s radius should be even smaller that He's radius given that Li+'s nucleus carries 50% more positive charge, and therefore, should pull in the 1s electrons even closer.

Can anyone help point me towards an answer? My only thoughts are that the two 1s electrons in Li+ must have more freedom to jump up to the 2s level than do those of He.  Is this going down the right path or am I completely off base?

[Corribus]

Usually atomic and ionic radii are determined experimentally with crystal structures or other spectroscopic data. Insofar as noble gasses (gases?) like helium do not typically form compounds, by virtue of their inertness, other methods have to be used to estimate them, and it doesn't always make sense to compare the estimates to experimentally determined ionic radii of other elements.

Where are you getting your values of 76 pm and 31 pm from?  It's important not just to look at numbers, but how those numbers are calculated or measured, to make sure you are comparing apples to apples.

[Fobbit]

That is a good point about how the radii of elements that do not form compounds are estimated; however, you can find other examples that also demonstrate this phenomenon across the ionic and atomic radii tables.

I've looked at several sources to confirm the ionic vs. atomic radii of the various elements and have found these estimates consistently across multiple sources. It is true, though, that I have not gone further to look up the root data from which these tables were generated.

The Li+ radius is over twice the estimated radius for He so I think it is more than just an estimation error. I suspect that having the additional proton in the nucleus is providing more freedom for the two 1s electrons to jump back and forth between the 1s subshell and the 2s subshell; however, this is only my hypothesis.

I greatly appreciate your input.

[magician4]

there is no such thing like electrons "jumping" from one place to another: this would be the darkest ages of early chemistry, Bohr's model, wrong, dead, buried and rotten by now

electrons are standing WAVES in the experiment "under the influence of an atom's nucleus"
their center of gravity is exactly IN the nucleus, and it remains there
, no matter what special wave function is used to describe their "orbitals"

... and hence everything derived from this false assumption, including all the questions and irritations resulting thereof, are meaningless


regards

Ingo

[Fobbit]

OK, Ingo, I understand that the Bohr construct is a model that is outdated, just as the standing wave construct will also, likely, be modified in the future. All of these are models, afterall, to describe what has been empirically observed or mathematically derived. Yet, the photoelectric effect is still observed. We still can excite electron "waves" to higher energy states which they can then fall (jump) back from releasing energy. I do not think the older construct is without conceptual merit.

That being said, I do not dispute where the center of mass of the electron's "wave" is. I am not sure it is germane to the observation I brought up for discussion. What I am asking for clarification on is why the functional diameter of Li+ is so much larger than He (as Na+ >> Ne; K+ >> Ar).

 

[Corribus]

What are you defining as "functional diameter"? Electron wavefunction probability density for every orbital extends out to infinity in every direction.

[Fobbit]

I agree that, theoretically, every atom's diameter is possibly infinite; however, even in a quantum world, the probability of an electron being 1 meter away from its nucleus approaches zero.

In a real world situation, for example, when examining a crystal's structure, there is a finite distance that is within a narrow range can be used to calculate an atoms radius. You can search for many modern chemistry texts, including some of those sited at the top of this forum, that contain reference charts to an atom's radius. I note it is not infinity across the periodic table, but rather some specific value that may represent a 95%, 99% or other arbitrary, but practical, limit for where we say the "functional" limit of the predicted edge of an atom (or ion) is.

 

[magician4]

(...) just as the standing wave construct will also, likely, be modified in the future.

I would be pretty eager to learn what deeper scientific insight of yours would probably be the foundation of this presumption . Did I miss something important in physics lately?
Mind you: Newton got refined, even Einstein and Schroedinger might become refined someday ...
...but Bohr was DISMANTELED!

We still can excite electron "waves" to higher energy states which they can then fall (jump) back from releasing energy.

does the string of your guitar completely jump elsewhere when you pick it, or does it just change its frequency?

Yet, the photoelectric effect is still observed.

yes, it is.
so what? do you need radii for this?
quantummechanics has an answer for this, too!

I do not think the older construct is without conceptual merit.

The earth being 6000 years old also has its merits to some people, yes, and electrons orbiting the nucleus did win Bohr the Nobel price, you have to give him that, yes.
However, the times they are'a changin' , and better insights prevail...

What I am asking for clarification on is why the functional diameter of Li+ is so much larger than He (as Na+ >> Ne; K+ >> Ar).

even this question is meaningless, as long as you don't tell us in which respect you want "functional diameter" to be understood. 95% theoretical electron density in orbitals? distance in some representative compounds? co-volume in van-der-Waals equation? ..( you name it)

asides from this:
"Distance" , "radius" (...) only is meaningfull with respect to distance between nucleii, as they are still well-defined with respect to "place" to give it a meaning.

everything else is misconception ( though still pretty much in use, I admit, and a source of much confusion at that)

[Corribus]

I don't think it's necessary to impugn Bohr to that extent.  After all, his model, though ultimately wrong because it's still semiclassical, did pave the way for our understanding of quantization.

My point was that there's no such thing as a discrete "atomic radius".  Anywhere you draw the line is going to be arbitrary, because electron density is a continuous function extending to infinity.  The atomic or ionic radius is determined experimentally by taking the mean bond length between two atoms and cutting it in half.  There is moreover a large variation in reported values depending on the criteria you use to make that determination.  Noble gasses don't (usually) form molecules, so there's no way to experimentally determine the "atomic radius" by this method. Therefore any comparisons between experimental values and estimated ones may not be 100% germane, particularly without knowing how the respective values were calculated or experimentally determined.

We do know that a higher nuclear charge does tend to lower the mean distance for an electron in a given orbital from the nucleus.  You can project this easily and exactly in hydrogenic atoms.  There's nothing unusual  going on between lithium and helium.  I maintain it's an artifact of the way you're comparing numbers - specifically, you're comparing apples to oranges.

[magician4]

After all, his model, though ultimately wrong because it's still semiclassical, did pave the way for our understanding of quantization.

just for the sake of historical truth: Bohr didn't commit absolutely nothing  to quantization.

The merits for this , foremost and in first place , go to Max Planck - and maybe Albert Einstein after him, broadening Planck's understanding from " the exchange of energy is quantitized" to "the energy itself, by its very nature, is quantitized (and hence, as a consequence , every exchange of it has to be, too)"

everything downstream from this, with electrons rotating at a frequency obeying Planck's law  (hence the quantum numbers n ) , with revolving electrical charges not radiating and all those other brute postulates of Bohr might have been interesting, even fascinating at a time - but are misconceptions, plain and simple.
... and even his explanation of emission spectra was based on the work of J.J. Balmer,  who had invented the respective quantitative equations earlier. All that Bohr committed here was, to (wrongly) claim that a "quantum jump" should be responsible for this, in that the electrons should be shifting to higher orbits ( or jump down from those, respectively). However, the merits for connecting Bohr's qualitative ideas to something that quantitatively could be calculated and meet reality, hence Balmer's observations / equation,  go to Arnold Sommerfeld: without him, Bohr's theory would have remained unable to quantitatively explain for real, observed spectra.

According to the Danish science historian Helge Kragh *⁾, even Bohr knew to be wrong in very central aspects of his own theory, and hence was modest enough to call his ideas "just the beginning of a for real understanding of atoms"

This, we should give to him, I agree


regards

Ingo


*⁾
as , for example, published in his book «Niels Bohr and the Quantum Atom»