The master equation is solved analytically for the ionization in a dense hydrogen plasma involving single-quantum transitions. The derived expression for the observed ionization rate coefficient is valid for all temperatures at which the ionization time constant is long compared with the internal relaxation time constants. At high temperature, the observed ionization rate coefficient is determined by excitation and ionization from the ground level. At low temperature, a bottleneck occurs above the first excited state, and the expression reduces to a form foreseen by Bates as the counterpart to the network-like expression for recombination. The implications with regard to the temperature dependence of the rate coefficient are discussed.