A rocket functions by ejecting mass out the back at high speed. By conservation of momentum, the rocket then accelerates. You want to optimize for velocity gai

A rocket functions by ejecting mass out the back at high speed. By conservation of momentum, the rocket then accelerates. You want to optimize for velocity gain (also known as delta-v) per unit mass of propellant. So the question is, should you eject something heavier at lower speed, or something lighter at high speed? Which is more efficient? If you write out the equation for a rocket ejecting some propellant at some velocity, apply conservation of momentum, and solve for the ratio of delta-v to propellant mass (just a bit of high school physics), it turns out that a higher exhaust velocity makes a more efficient rocket. As a sibling post points out, if you compare water vapor with hydrogen at the same temperature, hydrogen will have the higher velocity. Chemical rockets usually produce water and/or carbon dioxide, which are bigger molecules and therefore less efficient propellants than hydrogen. So if you have a way to heat hydrogen to the same kinds of temperatures you get in rocket exhaust — say, in a nuclear reactor — that’ll make a more efficient rocket. There are of course considerations other than pure efficiency. Our most efficient rockets, ion engines, are indeed crazy efficient, but their thrust is measured in milli-newtons or newtons. They can’t be used to lift things off earth. They also use propellants like krypton and xenon, presumably because they’re easier to store than hydrogen.