There are different Isotherms but most commonly used ones are Langmuir and Freundlich. Find attached the articles below as guide

Yes. Why not?

I think you are talking about two different things. Adsorption is different to absorption.

Photocatalytic degradation of dyes occurs under the action of light. Nanoparticles, for example, titanium dioxide will play the role of catalysts for the decomposition of dyes, since dyes are well adsorbed and reduce the activation energy of reaction.

To determine the adsorption isotherms of the dye on the visible spectrum, you need to remove the spectrum of the dye of a certain concentration before adsorption. Determine the intensity of the maximum absorption band and compare it with the intensity after adsorption. Intensity is proportional to concentration. Having a calibration graph of intensity-concentration you can determine the concentration of adsorbed dyes by the absorption spectrum and build an adsorption isotherm.

hey Peter Farrington could you elaborate?

The thing is that photo-active nanomaterials on being irradiated by suitable photon energy can produce reactive oxygen species in aqueous system which can break down the dyes of your concern and you can observe a faded color of the dye. However, the nanomaterials can act as very good sorbents which could adsorb a substantial amount of dye and it's derivatives from your solution at the same time. So, to comprehend the photocatalytic performance of your nanomaterials, you should carry out the same sets of experiments in dark and in lights. Coming to your main query, you can use the UV-vis spectrophotometric data to have the values of concentrations of your dyes after treating them at different conditions. These data have to be considered as Ct or Ce to calculate qe.

As Yuri described, the dye is aDsorbed onto the nanoparticle and the photodegradation occurs when light is aBsorbed.

the following attachment may help you

thanks a lot Yuri Mirgorod . Exactly what i was looking for!

yeah Peter....i almost skipped that part thanks for reminding me. great help @ Peter and Ali Asghar

yes it is possible. First you have to get the raw adsorption data for the dye which means the initial and equilibrium concentration of the dye. Then the obtained data will be fitted to the Langmuir or Freundlich adsorption isotherm models. The best fit will tell you the kind of adsorption that is taking place between the adsorbent and the adsorbate. for more information you can access

Removal of methylene blue (Mb) dye from aqueous solution by bioadsorption onto untreated Parthenium hystrophorous weed

and

Removal of Zn (II) and Cu (II) Ions from Aqueous Solution by Dried Prosopis JULIFLORA