Modern physicists are seriously trying to couple quantum mechanics and general theory of relativity. Even some scientists are trying to formulate a quantum theory of gravity. The subject of black hole physics is still under development. Accelerating model is putting all the scientists in a dilemma. Large number hypothesis or string theory or SUSY or quantum gravity or SM no model is throwing light on the secrets of ?fermi scale'' atomic and gravitational unification. Now a days particle physicists are trying their level best in estimating the ?strong coupling constant''. QCD is a highly complicated model. Scientists are spending million dollars on particle accelerators, super novae observations and dark energy probing projects. In this critical, highly sensitive and most expensive situation authors made a simple (theoretical) attempt to understand the secrets of cosmology, grand unification and Avogadro number. Even though the proposed ?atomic gravitational constant'' is having a large value it is naturally coupling the observed atomic, nuclear and particle physics constants accurately. Authors humbly request the whole science community to kindly look into this new approach.