The objective of this paper is to analyze the influence of the Coriolis force and internal heat source on Rayleigh-Bénard convection in a Boussinesquian fluid of depth d. A linear theory which is oriented towards the normal mode analysis technique is used for this mono-diffusive convection in order to find the criteria for the onset of Rayleigh-Bénard convection. The eigenvalue of the said problem was obtained by the use of the Galerkin method in the cases of rigid-rigid, rigid-free, and free-free velocity boundary combinations considering the isothermal and adiabatic temperature boundaries that determine the stability of the system. The effects of various parameters, Taylor number and the internal Rayleigh number are put under consideration only for stationary convection. Treating Taylor number as a critical parameter, shown that it plays a major role in stabilization of the system in case of any particular infinitesimal disturbance. The destabilization of the system has been possible with rotation by treating internal Rayleigh numbers as a critical parameter since the increase in values of the internal Rayleigh number advances the onset of convection.Oscillatory convection seems highly improbable as the scaled frequency of oscillation remains less than 0 for all combinations of Prandtl number, internal Rayleigh number, and Taylor number.