  This paper is concerned with the Schr\"odinger equation for atoms and ions
with N=1 to 10 electrons. In the asymptotic limit of large nuclear charge $Z$,
we determine explicitly the low-lying energy levels and eigenstates.
  The asymptotic energies and wavefunctions are in good quantitative agreement
with experimental data for positive ions, and in excellent qualitative
agreement even for neutral atoms ($Z=N$). In particular, the predicted ground
state spin and angular momentum quantum numbers ($^1S$ for He, Be, Ne, $^2S$
for H and Li, $^4S$ for N, $^2P$ for B and F, and $^3P$ for C and O) agree with
experiment in every case.
  The asymptotic Schr\"odinger ground states agree, up to small corrections,
with the semi-empirical hydrogen orbital configurations developed by Bohr, Hund
and Slater to explain the periodic table. In rare cases where our results
deviate from this picture, such as the ordering of the lowest ${}^1D^o$ and
${}^3S^o$ states of the Carbon isoelectronic sequence, experiment confirms our,
not Hund's, predictions.
