The source of the broad radiation of fast hydrogen atoms in plasmas containing noble gases remains one of the most discussed problems relating to plasma-solid interface. In this paper, we present a detailed study of Balmer lines emission generated by fast hydrogen and deuterium atoms in an energy range between 40-300 eV in a linear magnetised plasma. The experiments were performed in gas mixtures containing hydrogen or deuterium and one of the noble gases (He, Ne, Ar, Kr or Xe). In the low-pressure regime (0.01-0.1 Pa) of plasma operation emission is detected by using high spectral and spatial resolution spectrometers at different lines-of-sight for different target materials (C, Fe, Rh, Pd, Ag and W). We observed the spatial evolution for Hα, H β and Hγ lines with a resolution of 50µm in front of the targets, proving that emission is induced by reflected atoms only. The strongest radiation of fast atoms was observed in the case of Ar-D or Ar-H discharges. It is a factor of five less in Kr-D plasma and an order of magnitude less in other rare gas mixture plasmas. First, the present work shows that the maximum of emission is achieved for the kinetic energy of 70-120 eV/a.m.u. of fast atoms. Second, the emission profile depends on the target material as well as surface characteristics such as the particle reflection, e.g. angular and energy distribution, and the photon reflectivity. Finally, the source of emission of fast atoms is narrowed down to two processes: excitation caused by collisions with noble gas atoms in the ground state, and excitation transfer between the metastable levels of argon and the excited levels of hydrogen or deuterium.