For difference wavelength 60nm (Trp) with excittion 280nm we have seen max emission in 340nm. If the distance between the excitation wavelength (280) and emission wavelength (305) is about 25 nm, can it be said that this is related to an Trp amino acid?
Tryptophan fluorescence emission occurs in the 330-360 nm range, depending on hydrophobicity of the environment. The 305 nm emission could be tyrosine fluorescence, or it could be from Triton X-100 detergent if that is present.
Adam is most probably right in regards to Tyr. You excite at 280 nm, therefore no wonder you have Tyr fluorescence peak at 305 nm. On the other hand Tyr QY is even lower than Trp, so the question is of course, how many Tyr residues does your measured protein have? Trp extinction coefficient at an excitation of 295-297nm is much higher than that of Tyr and its fluorescence (ranges between 325 nm in the most hydrophobic environment to 360 nm in the most hydrophilic environment) and has a much higher QY than Tyr does, but in most proteins you will have fewer Trp than Tyr residues.
Why won't you try to excite your sample at 297 nm and measure fluorescence spectrum in the range 305 - 450 nm ? If you do, try working at a slightly higher concentration owing to the lower absorptivity in 297 nm.
Given that there are also the absorption spectra in the UV by second derivative of the proteins that can give precise indications on absorbing amino acids, you can try (if the amount of protein are so small that it cannot be useful for an absorption spectrum) also to run some excitation fluorescence spectra with emission at 305 or 350 nm. Coarsely they give similar information as the absorption. Tyr has a maximum absorption around 203-205 nm, while the trp at about 278-280, often with a pronounced shoulder at 292 nm. If your sample has a high absorption at 310-320 nm you have to suspect the presence of other chromophores. However, check also for the solution scatter, which often changes the spectral properties of protein fluorescence, thus you must always subtract a scan of blank sample.
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