At temperatures below 15 000 K, the major pathway for the electron impact dissociation of H₂ is through excitation to the b ³Σ_u⁺ excited electronic state. Total cross sections and energy differential cross sections for threshold energies as a function of vibrational states (v) for H₂ v = 0–4, D₂ v = 0–6 and T₂ v = 0–7 are calculated. The rates of dissociation as a function of electron temperature for each state are parametrized. Near-threshold rates are shown to be so critically dependent on the vibrational level that dissociation from very high-lying vibrational levels must be included in calculations of the rate at local thermal equilibrium (LTE) even at low temperature. An adapted version of the extrapolation procedure of Stibbe and Tennyson (1999 Astrophys. J. 513 L147) is used to approximate the rates for all of the higher vibrational levels, which are then used to calculate the LTE rate. The LTE rate is an order of magnitude greater than the v = 0 rate. Calculations of energy differential cross sections suggest that impact dissociation of vibrationally excited molecules could be the source of low energy H atoms observed in tokamak plasmas.