Context : The impulsive phase of solar flares is a time of rapid energy deposition and heating in the lower solar atmosphere , leading to changes in the temperature and density structure of the region .

Aims : We use an O V density diagnostic formed of the \lambda 192 / \lambda 248 line ratio , provided by the Hinode /EIS instrument , to determine the density of flare footpoint plasma at O V formation temperatures of \sim 2.5 \times 10 ^ { 5 } K , giving a constraint on the properties of the heated transition region .

Methods : Hinode /EIS rasters from 2 small flare events in December 2007 were used .
Raster images were co-aligned to identify and establish the footpoint pixels , multiple-component Gaussian line fitting of the spectra was carried out to isolate the density diagnostic pair , and the density was calculated for several footpoint areas .
The assumptions of equilibrium ionisation and optically-thin radiation for the O V lines used were assessed and found to be acceptable .
Properties of the electron distribution , for one of the events , were deduced from earlier RHESSI hard X-ray observations and used to calculate the plasma heating rate , within 2 semi-empirical atmospheres , delivered by an electron beam adopting collisional thick-target assumptions .
The radiative loss rate for this plasma was also calculated for comparison with possible energy input mechanisms .

Results : Electron number densities of up to 10 ^ { 11.9 } ~ { } { cm ^ { -3 } } were measured during the flare impulsive phase using the O V \lambda 192 / \lambda 248 diagnostic ratio .
The heating rate delivered by an electron beam was found to exceed the radiative losses at this density , corresponding to a height of 450 km , and when assuming a completely ionised target atmosphere far exceed the losses but at a height of 1450-1600 km .
A chromospheric thickness of 70-700 km was found to be required to balance a conductive input to the O V -emitting region with radiative losses .

Conclusions : Electron densities have been observed in footpoint sources , at transition region temperatures , comparable with previous results but with improved spatial information .
The observed densities can be explained by heating of the chromosphere by collisional electrons , with O V formed at heights of 450-1600 km above the photosphere , depending on the atmospheric ionisation fraction .