  For the first time, we have used RHESSI's spatial and energy resolution to
determine the combined chromospheric and coronal density profile of the flaring
solar atmosphere in a statistical manner, using a dataset of 838 flares
observable in hard X-rays above 25 keV. Assuming the thick-target beam model,
our "average flaring atmosphere" was found to have density scale heights of
131+/-16 km at low altitudes (chromosphere, up to ~1-1.5 Mm above photosphere),
and of 5-6 Mm at high altitudes (corona, above ~2-3 Mm). Assuming a unit step
change in ionization level, modeling yields a height of 1.3+/-0.2 Mm for the
transition between fully neutral to fully-ionized atmosphere. Furthermore,
centroids of emission above 50 keV, produced by electrons of similar or higher
energies, are located mostly in a small region ~0.5 Mm in vertical extent,
where neutral densities are beyond 3x10^13 cm^-3.
