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It is clearly a general trend that the atomic radii of the 3d elements in ascending order of atomic weight, leads to the following trend as in the graph below.

enter image description here

But, it was pointed out to me that, Mn has a higher metallic/ionic $[M^+]$ radius than chromium in reality, as given the radius values from literature.

How can this anomaly be explained?

The only thing different in Mn from Chromium is one proton more in the nucleas and the presence of 5 unpaired electrons(due to filled 4s orbital) in Mn, than in Cr(which has 6 unpaired electrons in 4s and 3d orbitals).

But again the 4s orbital is outside to the 3d orbital and therefore it is not contributing to the shielding, at least to an appreciable extent.

Please explain.

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The reason for your confusion may be the difference between atomic radius and ionic radius, as well as the specific comparison between ions that your source was making. Comparing manganese and chromium ions with the same charge, spin and coordination numbers, chromium ions are larger about half of the time (see http://abulafia.mt.ic.ac.uk/shannon/). However, since they didn’t seem to specify which ionic radius they were talking about, I suspect that whoever told you that manganese ions were larger was comparing the two elements in their most stable and common oxidation states, and $Mn^{2+}$ ions are indeed larger than $Cr^{3+}$.

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