The force responsible for holding electrons in orbit around the nucleus is called electromagnetic force. This fundamental force arises from the interaction between positively charged protons in the nucleus and negatively charged electrons. According to quantum mechanics, electrons exist in orbitals around the nucleus, where their energy levels dictate their distance from it. The balance between the inertia of the electrons and the attraction from the nucleus keeps them in stable orbits, which is essential for the integrity of atoms and the formation of molecules.