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The definition of atomic radius is half the average internuclear distance of an atom.

But many times I've been told that it is not possible to handle a single atom. Thus how can we measure the internuclear distance of an atom?

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As you told it is not possible to measure the inter nuclear distance of single atom. But here internuclear distance does not mean diameter of a single atom but it means distance between nucleus of two atom of same element.

enter image description here

This internuclear distance can be determined by two methods:

  1. X-rays method
  2. Spectroscopy method

Note: Atomic radius is not a set value for a given atom. Eg. $\ce{Fe^{+2}}$ ion have different atomic radius than $\ce{Fe+}$. Moreover, $\ce{Fe^{+2}}$< $\ce{Fe+}$

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  • $\begingroup$ I think it is important to note also that atomic radius is not a set value for a given atom. For example, Fe2+ ions have a different atomic radius than Fe3+ or Fe in metal. When we talk about atomic radii in minerals (which are crystalline) then there can be many different radii possible. You can find tables of these radii in mineralogy texts where they've been determined as the spherical size of the atom that fits into its site in the crystal. $\endgroup$ – ZSG Oct 29 '14 at 22:27
  • $\begingroup$ I think OP what to know the practice method of determining atomic radius, but we can add this as note. :-) $\endgroup$ – Freddy Oct 30 '14 at 4:32
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    $\begingroup$ Also, I'd rather stress that atoms do not "look" clear-cut as in the picture, but rather blurry, so even the specific atomic radius of an atom in a particular state is somewhat less definite than it might seem. $\endgroup$ – Ivan Neretin Feb 26 '16 at 6:26
  • $\begingroup$ @ZSG - It is more basic than that. The $\ce{Fe^{3+}}$ ion really has a different sizes in $\ce{FeCl_3}$, $\ce{FeBr_3}$, and $\ce{Fe_2S_3}$ for example. $\endgroup$ – MaxW Sep 30 '17 at 5:57