Atomic radii


by elas
Tags: atomic, radii
elas
#1
May15-03, 12:36 AM
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Can anyone tell me where to find Atomic Radii for Isotopes?
(All the tables I have found so far only list atomic radii for the 92 elements shown on the main table.)
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MrCaN
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#2
May15-03, 01:28 AM
P: 80
you can calculate them, roughly by multiplying the contents radii
damgo
#3
May15-03, 02:09 AM
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You want atomic radius, not nuclear radius, right? That's almost exactly the same for all isotopes of a given element.

Alexander
#4
May15-03, 07:11 AM
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Atomic radii


Yes, because the charge of nucleus is the same for all isotopes of given element, wave function of electrons spreads same way.
elas
#5
May15-03, 11:17 AM
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Perhaps I should be a little more frank. I have found a formula for producing Atomic Radii from mass and as Emsley,s 'Elements' and all the tables on the net do not give Atomic radii for isotopes I am hoping someone can give me an accurate figure so I can check my predictions.
As far as I am aware there is no formula for producing atomic radii accurate (to 4 decimal places), but as I am an amateur with no formal training I would appreciate comfirmation of that.
I seek to explain why element 92 is almost 300 times the mass of element 1 but only three times the size, according to Enc. Brit. this is one of the unsolved prolems of particle physics.
marcus
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#6
May15-03, 12:36 PM
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Originally posted by elas

I seek to explain why element 92 is almost 300 times the mass of element 1 but only three times the size, according to Enc. Brit. this is one of the unsolved prolems of particle physics.
I just consulted the CRC "Handbook of Chemistry and Physics" table of "Ionic Radii of the Elements"

this is not exactly what you were asking about because an ion, being charged, is not quite the same as a neutral atom

but it has at least some relation to your interest, I suppose.

All the figures were around one angstrom but they varied in what seemed like a quite irregular fashion.

A closer look showed more regularity if one considers only those ions with the same charge. For example uranium(+4) is the uranium atom missing 4 electrons and its radius is 0.97
and this can be compared with carbon(+4) also missing 4 electrons, which has radius 0.16

Here is a little table for you with some sizes of (+4 charged) ions:

carbon (+4) 0.16

silicon (+4) 0.42

germanium (+4) 0.53

tin (+4) 0.71

lead (+4) 0.84

uranium (+4) 0.97



Please quote an exerpt from the Encyclopaedia Britannica article which
you are using. I am curious to know the exact wording.
If the Britannica says something like this in connection with
particle physics (as contrasted with the physics of the atom)
then it suggests that they might have be talking about the
size of the NUCLEUS---damgo raised this issue.

Sorry i dont have information on the size of neutral atoms----tho I think they are all around one angstrom. Good luck in your search!
Alexander
#7
May15-03, 04:50 PM
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Originally posted by elas As far as I am aware there is no formula for producing atomic radii accurate (to 4 decimal places), but as I am an amateur with no formal training I would appreciate comfirmation of that.


I am curious if atomic or ionic "size" can even be defined to 3 digits accuracy. It is just a spread of outer electron wave function which strictly speaking is infinite.



I seek to explain why element 92 is almost 300 times the mass of element 1 but only three times the size...

Just because its outer electron does not see U nucleus as a charge +92, (thus U atom is not 92 times SMALLER than H one), but only as a charge about +2 - +3 or so.

If not Fermi repulsion of electrons, U atom would actually be 2-3 times smaller than H atom.



according to Enc. Brit. this is one of the unsolved prolems of particle physics.
Well, it is hard to calculate a wave function of an electron in multielectron atom with high precision. Too many of other electrons and of their messy mutual interactions to account for.
elas
#8
May15-03, 05:07 PM
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marcus Many thanks, this is getting close but unfortunately I had isotopes with mass but not radii, you have given radii but not mass.
Although it is not quite what I wanted it is in an area that I intended to tackle next because it shows the relationship between electrons and atomic radii. The change is in the expected direction but larger than expected. This supports those who claim that atomic nuclei sizes are related to the number of nucleons. Therefore changes in atomic radii are due mainly to changes in electron numbers. Which is another way of saying that quarks and electrons play the major part while the other constituents of the nucleons do no more than provide the basic structure.
marcus
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#9
May15-03, 06:05 PM
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Originally posted by Alexander
I am curious if atomic or ionic "size" can even be defined to 3 digits accuracy. It is just a spread of outer electron wave function which strictly speaking is infinite.
Just because its outer electron does not see U nucleus as a charge +92, (thus U atom is not 92 times SMALLER than H one), but only as a charge about +2 - +3 or so.
If not Fermi repulsion of electrons, U atom would actually be 2-3 times smaller than H atom.
Well, it is hard to calculate a wave function of an electron in multielectron atom with high precision. Too many of other electrons and of their messy mutual interactions to account for.
Alexander these are thoughtful and interesting comments!
As for the ability to define the ionic radius----it is an experimentally measured dimension specific to ionic crystals
as I understand it.

One measures a crystal and one counts the atoms in it and one determines the lattice spacings----then somehow one decides
on the ionic radius.

And in that case it must vary some from one sort of crystal to another. this at least is how I imagine the thing is defined and measured.

It seems significant to me that instead of calculating the ionic radius from QED and worrying about the fuzziness of the electron clouds one can simply put a bunch of atoms together in a crystal and SEE how close they pack and therefore---in a practical sort of way---how big they are
Alexander
#10
May15-03, 06:52 PM
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Well, both ways you get some fuzzines. Experimentally, say, Na in its own metal crystal and Na in table salt crystal have completely different wave function of outer (S) electron and slightly different p electron wave function, thus slightly different "size" of ion no matter how you define this size. Simply because it depends on environment. So I doubt that experimental "size" is more stable better than 2 digits.

Theoretical "size" (say, distance from nucleus ro which splits volume integral square of wave function 50/50 (inside/outside)) is calculable well (to 3+ digits) only for H atom (and H-like ions). Even He wave functions are so messy to calculate that various methods give various results in 3rd digit.
elas
#11
May16-03, 12:15 AM
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This is where my ignorance shows up, some tables show the measurement with a decimal point and some show the same number without the decimal point, which I assume means they are using different units of measurement.
However the key point is that, as far as I am aware, the measurements are found by experiment and no explanation has been put forward as to why most increases in the number of sub-atomic particles in an atom lead to a reduction in radius and only a few lead to an increase in radius.
I believe I am also correct in saying that to date there has been no explanation of the relationship between mass and radius but only between mass and density and I would like comfirmation of this please.
The relationship I discovered follows on from my discussions on the physics theory pages and from the work of rduncan and cannot be transfered to the physics pages which are correctly restricted to the standard model. That said it is necessary to come to the physics pages for advice and I greatly appreciate the advice received so far. Further clarification is requested on the points raised.
Many thanks
elas
elas
#12
May16-03, 12:26 AM
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I should add that I am using The Elements by John Emsley. Radii are given in three forms 'atomic', 'covalent', and 'van der Waals'
Alexander
#13
May16-03, 12:09 PM
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Originally posted by elas


....However the key point is that, as far as I am aware, the measurements are found by experiment and no explanation has been put forward as to why most increases in the number of sub-atomic particles in an atom lead to a reduction in radius and only a few lead to an increase in radius.

There is explanation, and you don't have to go futher than a good physical chemistry or good quantum chemistry textbook.

Explanation is quite simple - interplay of coulomb attraction to partially screened by other electrons nucleus and of Pauli repulsion of electrons.

In horizontal direction (from left to right) in Mendeleev's periodic table screening is decreasing (say, outer s- electron of Na atom sees nucleus as +1, but outer p-electrons of Cl see nucleus as +3 due to much less screening by other p- neigbor electrons than by inner electrons. That is why, by the way, Cl atom sucks electron so strongly that it tears it almost from any other atom - and we call such behavior of Cl (and F, Br, O) as "strong oxidizing".

So atoms gradually become smaller and smaller as you move from right side of periodic table to left side - due to increasing Coulomb force on outer electron.

When the shell is full (noble gases), then next electron has to start new shell and Pauli repulsion from electrons in previous shell makes its wave function way bigger. So from top to bottom of periodic table you have gradual increase in atomic radii.

Competition for lowest energy between pairs of p and d subshells, and d and f subshells belonging to different shells contributes into non-monotomy of radii charge of heavy atoms.
elas
#14
May17-03, 04:57 PM
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Alexander Thanks for reply. I checked with local library and it is not in the books I have access to.
I gather from the general tone of the replies that there is no firm statement of Isotope radii. As Emsley gives the radii for set conditions I assume that any isotope radii I produce using Emsley's data, would be subject to those conditions and I intend to see how far I can go in that direction.
I will post the results (or lack of results) within two weeks.
elas
Tyger
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#15
May17-03, 08:07 PM
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The size of an atom is determined by the outermost electron orbitals and is independant of the nuclear composition. The isotope data isn't given because it doesn't affect the size and therefore isn't important. That should answer your question.
elas
#16
May18-03, 04:38 PM
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Tyger
You have made the one statement that I can prove to be incorrect, is this your own opinion or is it the accepted view? If it is the considered opinion of experts can you please supply a reference.
elas
Tyger
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#17
May18-03, 11:26 PM
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Maybe it could be worded a little better. The number of neutrons in the atoms does not affect the size of the outer orbitals, which is what determines the size of atoms in a crystal lattice. Simple as that. An atom of U238 is the same size as U233 or U235, and that is why the data isn't supplied.
Thomas
#18
May19-03, 04:58 AM
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For all neutral atoms, the outer electron has roughly the same distance from the nucleus (about 1-2 Bohr radii). This is because if you have for instance an atom with 50 protons and 50 electrons, 49 of the electrons will shield 49 protons, so the situation is similar to hydrogen with 1 electron 1 and proton. The exact value varies within a factor 2 or so because of the interaction of the electrons (however, for highly excited states (where the outer electron is very far away from the nucleus) the coincidence is almost exact).

The same should also hold for a given degree of ionization, i.e. atoms that have the same number of electrons missing, although here the outer electron will be closer because of the stronger Coulomb force.

In any case, the number of neutrons (i.e. the isotope) can not possibly have an effect on the atomic electrons as they don't interact electrostatically.


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