X-ray photoelectron spectra of gases

We have seen above how X-ray photons may eject an electron from the core orbitals of an atom, whether it is free or part of a molecule. So far, in all aspects of valence theory of molecules that we have considered, the core electrons have been assumed to be in orbitals which are unchanged from the AOs of the corresponding atoms. XPS demonstrates that this is almost, but not quite, true. 

Question. For X-ray photoelectron spectra of a mixture of acetone and carbon dioxide gases, explain what you would expect to observe regarding the relative ionization energies (binding energies) and intensities in the C Is and O Is spectra. 

The intensities reflect the number of carbon atoms in each position. Comparing the C Is signals from CO2 and from C=0 shows that the mixture of gases is almost equimolar. The C Is signal from the methyl groups of acetone should then have twice the intensity of the other two signals because the carbon atoms are symmetrically equivalent. 

The spectrum below shows that the O Is binding energy is higher for CO2 than for acetone but there is no simple explanation for this. The spectrum shows that, in this case, the mixture contained considerably more (more than twice as much) acetone as CO2 because the O Is signal would be twice as strong as that for acetone in an equimolar mixture. 

The XPS chemical shift, for an atomic core orbital with principal and orbital 

The XPS chemical shift, AEnl, for an atomic core orbital with principal and orbital angular momentum quantum numbers n and L respectively, in a molecule M is given by 

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