I am doing temperature emissivity correction. I am wondering which would be the correct value to use as the wavelength of emitted radiance in Landsat 8 band 10. Will it be correct to use 10.8 micrometers as the wavelength or the raw band 10 raster? I am asking this because I think 10.8 micrometers are an average while band is likely to be a much more precise value.
I am not sure I understand the question. To do any radiometrically accurate calculation you would need to do it at higher spectral resolution, say in steps of 50 nm within the entire bandwidth of the TIRS band 10 channel and take into account the spectral response function of this channel. Not sure what do you mean by "band", but if it is really the DN-value in a Band 10 image as you state in your question, this has nothing to do with wavelength since the DN is calibrated radaince in arbitrary units.
I guess it is better to look at the curves provided by USGS for both sensors and then decide if those suit your needs. Also check if the provided formulas for DN to at sensor radiance conversion give similar results for one and the same object.
There are many thousands of DN (Digital Number) values in a LANDSAT 8 TM spectral band. Low DN are low values of emitted energy in the Thermal IR band and high DN are high values of emitted energy in the thermal band. There are two thermal bands in the L8 sensor, I believe, whereas the L7 and earlier TM sensors all had only one thermal IR band.
wavelength of emitted radiance for band 10 is 10.8
wavelength of emitted radiance for band 11 is 12
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