Explain Effect of Concentration, Particle size & Wavelength on Scattering?

i) Effect of Concentration on Scattering:

The attenuation of a parallel beam of radiation by scattering is given by $$I_t=I_0{e}^{-Jl}$$ $$\log \frac{I_0}{I_t}=KlC$$ $$whereK=\frac{J}{2.303C}$$ Where $I_0$ and $I_t$ are the intensity of the beam before and after passing through the length $l$ of a turbid medium. The quantity $J$ is called turbidity coefficient. Its value is often found to be linearly related to the concentration of the scattering particles. As a consequence, a relationship similar to Beers Law is,

ii) Effect of Particle size on Scattering:

The fraction of radiations scattered at any angle depends upon the size and shape of particles responsible for scattering. Those factors which influence the particle size at the time of precipitation in gravimetric, also affect both turbidimetry and nephelometry. Thus gravimetric factors such as the concentration of reagents, rate, and order of mixing, temperature, pH and Ionic strength are important Experimental variables. For proper scattering see that particles size must be uniform.

iii) Effect of Wavelength on scattering:

It has been shown experimentally that the turbidity Coefficient varies with wavelength as given by the equation $J=S{\lambda }^{-t}$ Where S is Constant for a given system. The quantity t depends on the particle size and has a value of 4 when scattering particles are smaller than the wavelength of the radiations incident on it. For particles with a dimension similar to wavelength, $\lambda$ is found to be 2. For purpose of analysis ordinary white light is used, but if the solution is colored then we have to select that wavelength so that absorption by the medium is minimum.