Barium atoms at the surface of large argon clusters are excited into the 6s6p(1)P(1) state leading either to ejection and subsequent fluorescence of the free barium atom or to fluorescence of solvated barium. Relative probabilities for these two processes as a function of the excitation energy and of the cluster size are presented. By comparison with the binding energy from a molecular dynamics (MD) calculation, we find that the barium atom is not excited above the limit for direct dissociation. The nonzero desorption probability is attributed to the gain of surface energy of the argon cluster which is partially transferred to the barium atom. Using linearly polarized laser light for the excitation, a positive polarization of the fluorescence of the ejected barium atoms is observed, whereas the polarization fluorescence of the solvated barium is negative. This indicates that the solvated barium atoms undergo a relaxation process which rotates the orientation of the excited orbital before the fluorescence. The degree of polarization of the fluorescence from ejected barium does not depend on the excitation energy or the cluster size.