Second orbit

You can easily prove with number theory that the number of orbitals in an atom's n-th orbit is : $n^{2}$
Therefor, since in each orbital there can be at most 2 electrons, the maximum number of electrons is : $2n^{2}$
For $n=2$ we find that the maximum number of electrons in an atom's second orbit is : $\boxed{8}$