A fission thermal hydrogen rocket uses fission to heat hydrogen propellant. It
has a higher exhaust speed than chemical rockets (13 km/s vs. 4.4 km/s). It is in the sweet spot between chemical rockets and electric rockets (see the plot).
Rocket type Exhaust speed (km/s)
Nuclear: Fission thermal hydrogen 13
Chemical: Hydrogen + Oxygen 4.4
Chemical: Methane + Oxygen 3.7
Chemical: Kerosene + Oxygen 3.3
Chemical: Solid fuel 2.7
Hydrogen is used for its low mass. The lower the mass of the propellant molecule, the higher the
exhaust speed.
Exhaust speed is determined by temperature. For a temperature of 2750 Kelvin, the speed of monatomic
hydrogen propellant is 13 km/s.
Fission thermal rockets are easy to design. Baffling that we don't already have them.
A fission electric uses fission to produce electricity, and it uses electricity to propel ions. The power/mass of an electric rocket is limited by cooling to 200 Watts/kg, which is too feeble to move large stuff around. It's good only for small spacecraft on long-term missions.
A fission thermal rocket can achieve a higher power/mass because it uses hydrogen exhaust for cooling.
Fission-thermal rockets are for deep space. They don't have enough power/mass for launch, or to use the Oberth maneuver. Only chemical rockets have sufficient power/mass.
https://www.jaymaron.com/astronautics.html#thermal