Hydrogen can be both stable and unstable at the same time, depending on several key factors.
Hydrogen is unstable in its natural state from the point of view of chemical stability.
This is due to the fact that hydrogen has one electron in its lowest energy level, indicating an unstable arrangement. This makes it highly reactive, and hydrogen undergoes several reactions to obtain a stable electron configuration.
The energy level of an atom can be either empty or full of electrons.
Hydrogen isotopes such as protium and deuterium are extremely stable.