The numerical solution of the Darcy-Forchheimer flow of a Williamson nanofluid across a spinning disc is discussed in this paper. This issue took into account the existence of mobile microorganisms and the consequences of radiation exposure. Parameters were used to build the fundamental governing equations, and then these partial differential equations were transformed into ordinary differential equations using the appropriate similarity transformations. The BVP4C is then used to perform a numerical solution of these equations. Several factors' impacts on tangential and radial velocities, temperatures, concentrations, and motile microorganisms were explored, along with their corresponding visual representations. The physical implications of the findings are also elaborated on in great detail.