How can the atomic radius of any atom be accurately calculated?

[omax]

hello, I was wondering how the atomic radii where calculated.
I have used the formula r=\frac{a_{o}n}{z*/n*}

where z* is effective nuclear charge
and n* is the effective principal quantum number
but it seems to give me a bit different radii compared to the ones on Wikipedia http://en.wikipedia.org/wiki/Atomic_radius

so can anyone be kind enough to tell me an equation from which I can calculate the atomic radius of any atom. I couldn't find any on the net.

by the way this is my first post :D

and thanks

 

[Meir Achuz]

That formula is only for single electron atoms. With more electrons, the calculation is much more complicated, but the radius is usually about half an Angstrom.

 

[omax]

so can you please let me know the formula or just give me a helpful link.

 

[cgk]

OP, this does not work:
(i) atoms do not have sharp boundaries. What is an "atomic radius" is a matter of definition, and many exist for different purposes (e.g., can der Waals radius, covalent radius, "radius at which the electron density falls below value xxx"), etc.

(ii) even if you have a clear definition, calculating its actual numerical value requires an approximate solution of the atomic Schrödinger equation. That can, in practice, only be done by specialized software (quantum chemistry packages, e.g., Molpro, Orca, Gaussian) which implement methods like Hartree-Fock or Kohn-Sham density functional theory. The result is not a simple formula.

 

[UltrafastPED]

Just look up the distances between atoms in various crystals. The distances vary with the crystal axis followed.

This is one "definition" of atomic size - it tells you how many fit in a certain space when packed together as a crystal of that type.

See http://en.wikipedia.org/wiki/Crystal_structure
and http://www.kayelaby.npl.co.uk/chemistry/3_7/3_7_7.html

You will even find some formulas ... but not the one you seem to be looking for.

 

[ZapperZ]

so can you please let me know the formula or just give me a helpful link.

The "real world" often has no one simple formula. The larger the atom, the more complexity it can have. By the time you get beyond the He atom, a lot of the description of the atom are based on approximations and calculation/computational schemes, as described by cgk.

Zz.

 

[omax]

anyway thanks for answering, although I did not get what I was looking for...

 

[sankarshana016]

You could calculate the Bohr Radius of an atom, although it only applies to single electron species(like Hydrogen)

R=(n^2*h^2ε0)∏mZe^2

Where,
n=orbit number
h= Plank's constant
ε0= Permittivity of Free Space
m=mass of an electron
Z= Atomic number
e= Electronic Charge

 

[ZapperZ]

You could calculate the Bohr Radius of an atom, although it only applies to single electron species(like Hydrogen)

R=(n^2*h^2ε0)∏mZe^2

Where,
n=orbit number
h= Plank's constant
ε0= Permittivity of Free Space
m=mass of an electron
Z= Atomic number
e= Electronic Charge

Did you even read the first post of the thread to figure out the problem?

...but it seems to give me a bit different radii compared to the ones on Wikipedia...

This was the whole point of the OP's question, that this simplistic model doesn't work for actual atoms!

Zz.