The effect of radiation-induced dissociation of hydrogen gas in nuclear rockets is studied. The degree of dissociation is obtained by solving rate equations, which include the fast ion-induced dissociation and ionization of atomic and molecular hydrogens. Analytical formulas are used to estimate a change in the viscosity and the specific impulse. We have found that the fast ion-induced dissociation can theoretically play a role in enhancing the specific impulse for nuclear rocket concepts using hydrogen gas at low pressures (0.1 MPa) and low temperatures (3000 K). It is also shown that the specific impulse is enhanced by mixing helium-3, lithium-6, and boron-10 with hydrogen.