We study a time-dependent hydrogen ionization in the atmosphere of SN 1987A during the first month after the explosion. The model includes kinetics of hydrogen ionization and excitation, molecular hydrogen kinetics, and a time-dependent energy balance. The primary strong effect of the time-dependent ionization is the enhanced hydrogen ionization compared to the steady-state model. The time-dependent ionization provides a sufficient population of excited hydrogen levels to account for the

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... d H-alpha without invoking the external Ni-56. We find that the Ba II 6142 A line in SN 1987A can be reproduced for the LMC barium abundance. This resolves the long-standing problem of the unacceptably high barium overabundance in SN 1987A. The key missing factor that should be blamed for the "barium problem" is the time-dependent ionization. The modelling of the H-alpha profile on day 4.64 indicates the ratio of the kinetic energy to the ejected mass about 0.83 10^50 erg/Msun.