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Nitric acid oxidizes iodine to iodic acid, $\ce{HIO3}$ and not periodic acid, $\ce{HIO4}$, which is of a higher oxidation state. This happens although other nonmetals are oxidized to their highest oxidation state. How can this be explained?

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Nitric acid is not strongly oxidizing enough to get iodine to +7. Relativistic effects tend to make the $s$ subshell valence electrons more stable than the others in heavy atoms (http://www.annualreviews.org/doi/abs/10.1146/annurev-physchem-032511-143755), so to some extent iodine acts as if it has only five valence electrons. To pull out those last two electrons and get periodic acid, electrochemical oxidation is commonly used with a very high oxidation potential (https://en.wikipedia.org/wiki/Periodic_acid).

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