The formation of hydrides by gas-phase reactions between H2 and a heavy element atom is a very selective process. Reactions with ground-state neutral carbon, oxygen, nitrogen, and sulfur atoms are very endoergic and have high energy barriers because the H2 molecule has to be fragmented before a hydride bond is formed. In cold interstellar clouds, these barriers exclude the formation of CH, OH, NH, and SH radicals through hydrogen abstraction reactions. Here we study a very energetically unfavorable process, the reaction of N(4S) atoms with H2 molecules. We calculated the reaction rate coefficient for H2 in different vibrational levels, using quantum methods for v = 0−7 and quasi-classical methods up to v =12; for comparison purposes, we also calculated the rate coefficients of the analogous reaction S (3P)+ H2(v) → SH + H. Owing to the high energy barrier, these rate coefficients increase with v and also with the gas temperature. We implemented the new rates in the Meudon photodissociation region (PDR) code and studied their effect on models with different ultraviolet (UV) illumination conditions. In strongly UV-irradiated dense gas (Orion Bar conditions), the presence of H2 in highly vibrationally excited levels (v ≥ 7) enhances the NH abundance by two orders of magnitude (at the PDR surface) compared to models that use the thermal rate coefficient for reaction N(4S) + H2 → NH + H. The increase in NH column density, N(NH), across the PDR is a factor of ~25. We investigate the excitation and detectability of submillimeter NH rotational emission lines. Being a hydride, NH excitation is very subthermal (Trot ≪ Tk) even in warm and dense gas. We explore existing Herschel/HIFI observations of the Orion Bar and Horsehead PDRs. We report a 3σ emission feature at the ~974 GHz frequency of the NH NJ = 12 − 01 line toward the Bar. The emission level implies N(NH) ≃ 1013 cm−2, which is consistent with PDR models using the new rate coefficients for reactions between N and UV-pumped H2. This formation route dominates over hydrogenation reactions involving the less abundant N+ ion. JWST observations will quantify the amount and reactivity of UV-pumped H2 in many interstellar and circumstellar environments.