What must be maintained for an electron to stay in orbit around an atom?

For an electron to remain in orbit around an atom, it must achieve a balance between the attractive force of the positively charged nucleus and its own kinetic energy. This stable state requires that the energy levels of the electron be quantized, meaning that the electron can only occupy specific energy levels without gaining or losing energy.

When an electron occupies a stable orbit, it is not radiating energy away, which would lead it to spiral inward and eventually lose its orbit. The concept of quantized energy levels ensures that electrons remain in defined orbits without the continuous need to gain or lose energy, thus maintaining their stable position around the nucleus. In essence, the electron's energy is fixed while in a particular orbit, which allows it to remain there without transitioning to other states unless influenced by external forces or interactions.