Hydrogen is the lightest chemical element. Its most common isotope (1H) comprises just one negatively charged electron, distributed around a positively charged proton (the nucleus of the atom). Thus, is the first element on the periodic table.
It is an odorless, tasteless, colorless, and highly flammable gas that burns at concentrations as low as 4% H2 in air, and even lower in pure oxygen.
In standard conditions hydrogen naturally forms the gaseous molecule H2, with a boiling point of 20.27 K (-252.88 °C) and a melting point of 14.02 K (-259.13 °C).
As Nuclear Rocket Propellant
It is used in nuclear rockets because lighter molecular travel at greater velocities at a given temperature and the propellant efficiency of a rocket known as specific impulse depends on the exhaust velocity. The current limit solid materials can obtain is around 5000 degrees Celsius and these materials are typically ceramics. Even using hydrogen as a propellant solid core nuclear thermal rockets do not make order of magnitude differences in mass fraction over chemical propulsion on short flights like a mission to Mars and the Moon.
As a Stable Chemical Fuel
Hydrogen is also the fuel of choice for the upper stage of chemical rockets both because hydrogen has the highest specific impulse of any stable fuels. Unfortunatelly, it also has the lowest density of all rocket fuels, and the highest cryogenic demands. This makes it feasible for multi-stage rockets, but not for a SSTO.
Suspending Hydrogen ions in H2
There has been some work to attempt to suspend hydrogen ions in hydrogen fuel to obtain far greater specific impulses. Although there are many challenges to using such a fuel, it has the potential to produce vastly more energy than the H2 + O2 burn.
Cryogenic hydrogen is extremely difficult to store because it has a tendency to boil off and escape. Because of this the hydrogen used to fill the external tank of the shuttle is not gilled until the day of launch to eliminate boil off. It is possible to reduce but not eliminate the boil off using a condenser but given the weight and power requirements of a condenser they are not used in space flight.
This makes it feasible for rockets than burn their hydrogen fuel in a short time after launch, but it's not feasible to be sent to Mars for example to be used for vehicle return, because boil off after such a long time (> 6 months) makes the lost in quantity considerable. Because of problems due to boil off sometimes methane is considered for the return flight of longer durations space missions such as a mission to mars.
Hydrogen in H2 form is extremely small and can easily escape between the space of high surfaces especially at high pressure. At extremely high pressures the challenges to store cryogenic hydrogen are immense because the cold hydrogen escaping though the spaces between solids can turn materials extremely brittle and susceptible to fractures.
Hydrogen In Space
Because hydrogen is so light it escapes easily from planets that don’t have sufficient gravity and are not protected from the solar wind. Thus there tends to be more hydrogen found in planets further away from the sun than near the sun. However it can be found in planets closer to the sun in water deep underground or within a permanently shaded crater. There is a limited amount of water on the Moon and there is believed to be significant amounts of water on Mars, though not as abundant as on Earth. The gas giants such as Jupiter are mainly composed of hydrogen.