Hydrogen molecules may have considerably high density in edge regions of fusion devices so that clarifying their behavior in edge plasmas is very important in understanding the phenomena near plasma facing materials. This paper evaluated the energy distribution of the dissociated products of H2 due to the electron induced excitation to the repulsive state b3Σu and the excitation to a3Σu followed by the radiative decay to the repulsive state b3Σu under the framework of Gryzinski approximation [M. Gryzinski, Phys. Rev. 138 (2A) (1965) A305, A322, A366]. The vibrational populations of H2 were considered in the calculation. The results show that the dissociated atoms from these channels are highly distributed in the low energy range (<1eV) while there is no significant distribution in the high energy range (>3eV), when H2 molecules are vibrationally excited. The discussions were made on the influences to Hα profiles in the low temperature plasmas [S. Tanaka, B.J. Xiao, K., Kobayashi , M. Morita, Plasma Phys. Control Fus. 42 (2000) 1091]. It is shown that the contribution of the low energy atoms in ground state may not be the only contributions of the low energy component in the observed Hα especially when H2(X1Σg+)+e→H2(1sσ,nlλ|1Λ)→e+H(1s)+H(2s) reaction has considerable reaction rates in the electron temperature around 10 eV.