Electrons do not stick to the nucleus due to the principles of quantum mechanics, specifically the uncertainty principle. If an electron were to be confined close to the nucleus, its position would be well-defined, leading to a high uncertainty in momentum and increased kinetic energy. Atoms prefer to be in low-energy states, so electrons occupy regions where their position is more uncertain, resulting in stable orbits at a distance. The quantum mechanical model describes the probability of finding an electron at various distances from the nucleus rather than defining a fixed orbital path. Additionally, there is a small probability that electrons can be found within the nucleus, which can lead to phenomena like electron capture in certain isotopes.