We present an experimental and theoretical investigation of K atom desorption from the basal plane of graphite at 83 K induced by low energy photons (3-6 eV). The 2D potassium overlayer is characterized by low energy electron diffraction (LEED), high-resolution electron energy loss spectroscopy (HREELS), thermal desorption spectroscopy (TDS), and work function measurements. At monolayer coverage (5.2 x 10(14) atoms cm(-2)), the dependence of the cross section on photon energy has a threshold at (h) over bar omega approximate to 3.0 eV and rises up to a maximum of 1.8 +/- 0.4 x 10(-20) cm(2) at 4.8 eV. The coverage dependence of the photoyield reflects the existence of two phases of adsorbed K, dilute ionized photo-active and close-packed photo-neutral, respectively. The observed photodesorption is a single-photon, nonthermal event, consistent with a substrate-mediated mechanism. The desorption results from attachment of optically excited hot electrons to the empty 4s state of ionized potassium. The theory predicts in this case a Gaussian line shape of the photoyield vs photon energy. Fitting the model parameters to the experimental data, we determine (i) the energy and slope of the excited state potential energy curve, and (ii) the position and width of the potassium-induced 4s resonance. The present findings combined with other available data for potassium on graphite are used to construct 1D potential energy curves along the surface normal for K+ and K-0. The calculated cross sections for s- and p-polarized Light are in qualitative agreement with the measurements.