A new spectroscopic method of determination of the degree of dissociation of hydrogen is proposed. The method is based on measurements of the relative intensities of two atomic lines of the Balmer series, H_α and H_β, and of one molecular line, the (2-2)Q1 line of the Fulcher-α system. These intensities are related to two plasma parameters: (i) the ratio of atomic and molecular hydrogen densities [H]/[H₂], connected with the degree of dissociation of hydrogen and (ii) the artificial parameter , characterizing a tail of an electron energy distribution function (EEDF) in the threshold region of electron impact excitation cross sections. The link between measured relative line intensities and plasma parameters was found in the framework of a most simple collision-radiative model taking into account only the direct and dissociative electron impact excitation and spontaneous decay of excited states. Numerical simulations made it possible to analyse main peculiarities and to estimate the range of the applicability of the method concerning numerical values of [H]/[H₂] and . For the first time, the fine structure of Balmer lines was taken into account in the spectroscopic determination of the degree of dissociation of hydrogen in non-equilibrium plasmas. The rate coefficients for electron impact excitation of the , v ≤ 2, N ≤ 1 rovibronic level of the hydrogen molecule were calculated with a Maxwellian EEDF for electron temperatures T_e ≤ 0.5-100 eV. Earlier calculated values of the emission rate coefficients for direct and dissociative electron impact excitation of H_α and H_β lines were extended for electron temperatures up to 100 eV.