In this paper, we accurately estimate the ground-state energy and the atomic radius of the helium atom and a helium-like Hookean atom by employing the uncertainty principle in conjunction with the variational approach. We show that with the use of the uncertainty principle, electrons are found to be spread over a radial region, giving an electron cloud. Our calculation also shows how the Coulomb interaction between electrons affects their distribution. This leads to a physical picture of how electrons are located with respect to each other in these atoms. Finally, we also obtain through our calculations a general formula for the estimate of ground-state energy and radius of two electron atoms and ions with atomic number Z. (Contains 4 figures.)