How it was observed, that elements in columns 6 and 11 assume abnormal electron configuration?
How it was observed, that elements in columns 6 and 11 assume abnormal electron configuration?


I assume you to mean


  How it was first observed, that elements in columns 6 and 11 assume abnormal electron configurations?


Chemists (starting with alchemists) have were doing stoichiometric reactions for a very long time. 

The point is that if there was only a single "normal electron configuration" for chromium, then there would only be one chromium chloride. However chemists have synthesized three. 


Chromium(II) chloride, also known as chromous chloride.
Chromium(III) chloride, also known as chromic chloride or chromium
trichloride
Chromium(IV) chloride


Thus the fact that there must be "abnormal" electron configurations was first discovered by stoichiometry, not spectroscopy. 

Other columns in the periodic chart do have elements with multiple electron configurations. So such an "abnormality" isn't unique. 



If your question means 


  How are the bonding energies measured for the elements in columns 6 and 11 in various electron configurations?


Then ESCA would be one technique.