Hydrogen is the main chemical component of the solar plasma, and H-ionization determines basic properties of the first adiabatic exponent ${\Gamma _{1}}$ . Its ionization significantly differs from the ionization of other chemicals. Due to the large number concentration, H-ionization causes a pronounced lowering of ${\Gamma _{1}}$ , with a strongly asymmetric and extending across almost the entire solar convective zone. The excited states in the hydrogen atom are modeled using a partition function, which accounts for the internal degrees of freedom of the composite particle. A temperature-dependent partition function with an asymptotic cut-off tail is derived from the quantum mechanical solution for the hydrogen atom in the plasma. We present numerical simulations of hydrogen ionization, calculated using two partition function models: Planck-Larkin (PL) and Starostin-Roerich (SR). In the SR model, the hydrogen ionization shifts to higher temperatures than in the PL model. Different models for excited states of the hydrogen atom may change ${\Gamma _{1}}$ by as much as $10^{-2}$ . The ${\Gamma _{1}}$ profiles for pure hydrogen exhibit a “twisted rope” structure for the two models, significantly affecting the helium ionization and the position of the helium hump. This entanglement of H and He effect provides a valuable opportunity to investigate the role of excited states in the solar plasma.
