For a two particle system in QM, if we have identical particles, which are fermions then we require that the overall wave function (position and spin) is antisymmetric and if the the particles are identical bosons then we require that overall wave function is symmetric, i.e.
$$\psi(r_{1},r_{2}) = A[\psi_{a}(r_{1})\psi_{b}(r_{2})\pm\psi_{b}(r_{1})\psi_{a}(r_{2}) ].$$
Question: But what are the rules when considering atoms. For example, helium or hydrogen seem to follow the fermion rules regarding when a wave function is symmetric or antisymmetric, that is the overall wave function should be antisymmetric. Do we follow the rules related to fermions for atoms as well since we have electrons involved? What is the basic motivation for these rules? I am just starting to learn about spin in QM, hence am using an introductory text.
Thanks.