1. Apr 2, 2014

### 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

2. Apr 2, 2014

### 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.

3. Apr 3, 2014

4. Apr 3, 2014

### 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.

5. Apr 3, 2014

6. Apr 3, 2014

### ZapperZ

Staff Emeritus
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.

7. Apr 6, 2014

### omax

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

8. Apr 12, 2014

### 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

9. Apr 12, 2014

### ZapperZ

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

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

Zz.