# Is it possible to calculate atomic radius with electron configuration?

I need to know whether is it possible to calculate the atomic radius according to the number of electrons and electron configuration. Or is there any way to calculate the atomic radius using common characteristics which an atom has?

• Welcome to chemistry.SE! You can visit the help center or take a tour of the site to get more familiar with our policies. Jan 18 '15 at 12:28
• You can find the effective nuclear charge ($Z^*$) using Slater's rule and then plug it into Bohr's formula ($r = \dfrac{53 n^2}{Z^*} \pu{pm}$). This value is quite close to the covalent radius.
– Shub
Aug 13 '21 at 15:27

## 1 Answer

There's no measuring the radius of a single atom, mainly because electrons are around the nuclei: We can't define a radius for any single atom. Take a loom at the uncertainty principle:

Introduced first in 1927, by the German physicist Werner Heisenberg, it states that the more precisely the position of some particle is determined, the less precisely its momentum can be known, and vice versa. The formal inequality relating the standard deviation of position $\sigma _x$ and the standard deviation of momentum $\sigma _p$ was derived by Earle Hesse Kennard later that year and by Hermann Weyl in 1928: $$\sigma _x \sigma _p \geq \frac{\hbar}{2}$$ Wikipedia

Thus, if you want to measure an atom's radius, you have to measure the distance between two nuclei, and then divide it by two. This results in different types of radius defined for atoms. The most common are covalent radius, ionic radius, and Van der Waals radius. Radii trends are what that are mostly studied in undergrad chemistry, rather than the how of measuring them with advanced techniques.

Chemguide is pretty informative when it gets to teaching the trends:

chemguide: atomic radius