A simple, computationally efficient 1D model is suggested for the recycling of atomic and molecular hydrogen between the main chamber first wall (FW) of a tokamak and the peripheral plasma. The model is based on iteratively solving the kinetic equation for the 1D velocity distribution function (VDF) of hydrogen neutral atoms in the projection of velocity on the direction normal to the FW. The model results in a fast-converging routine due to the domination of the contribution to the VDF from long-distance, ballistic flights of the neutral atoms produced by the charge exchange of colder atoms with hotter plasma ions. The proposed modification of the ballistic model (BM) enhances its original version along the following lines: the account of the inelastic reflections of the neutral atoms from the wall; parameterisation of the boundary condition for the VDF of the atoms produced by the reflection of ions from the wall with immediate recombination, without capture in the wall and thermalisation there; extension to a mixture of hydrogen isotopes; elaboration of algorithms for speeding up computation on graphical processing units. The complete set of equations of the BM is published for the first time. The model is verified by comparison with the EIRENE code simulations of the VDF of neutral atoms and molecules in the scrape-off-layer around mid-plane for typical conditions of ITER operation. The applicability of the BM to the synthetic diagnostics developed for the H-alpha high-resolution spectroscopy is demonstrated. That is, the simple 1D model reproduces reasonably well the 1D projection of the data computed with the 3D Monte-Carlo code on a 2D plasma background.