The vertical fraction variation of eddy diffusivity was taking into consideration in the dispersion of pollutants from a point source. A power-law profile was used to describe the variation of wind speed and vertical eddy diffusivity with height z above ground surface. The dry deposition of the diffusing particles at the ground surface is taken into account through the boundary conditions. The concentration of pollutants was derived assuming that the vertical diffusion is limited by an elevated inversion layer located at the top of the boundary layer “h". Also the decay distance of a pollutant along the wind direction was estimated. The resulting analytical solutions have been applied on the emission from the Research Reactor at Inshas in unstable condition and Hanford diffusion experiment in stable condition. Comparisons between proposed and observed concentrations show a good agreement between the proposed and observed concentrations when "α=0.81 " than others fractions and integer value. The results are discussed and presented in illustrative figures.