"Spicy world of NanoScience"
sir it is all depend on absorption edge of this material in spectra .
also make me clear from which technique you measured a particle size.
I think the value changes from the type of oxide you are dealing with. I have read few papers which report the value of alpha haematite as 2-2.2 eV. I am sharing a paper which reports that value.
You may want to look at this.
Iron oxides show diluted magnetic semiconducting (DMS) behavior. This will make them proper choice for spintronic or spinelectronic. If you synthesized nanoparticles of magnetite then you must have slit difference from bulk state band gap which is 0.14 eV. But for it's Quantum dot (below 10 nm in diameter) the band gap widened about your value 3.9 eV. However the Spectroscopy of these nanoparticle needed exact setting like scan rate, shadow and reference introduction and etc. If you did your Spectroscopy on substrate, I ask you try in colloidal state and be sure your solution concentration is in the range of Spectrometer device can Analysis it.
TMU optoelectronic lab.