In solids, electrons are typically bound to atoms and form a structure known as a crystal lattice. Quantum tunneling refers to the phenomenon where a particle can pass through a potential barrier, even if it does not have sufficient energy to overcome the barrier classically. This phenomenon arises from the wave-like nature of particles, as described by quantum mechanics.
In the context of electrons in a solid, quantum tunneling allows for the possibility of electrons moving through the crystal lattice, even when their energy levels are not sufficient to surmount the energy barriers imposed by the atomic potentials. However, it's important to note that the probability of an electron tunneling through the barrier decreases exponentially as the barrier becomes larger or thicker.
While there is a non-zero probability for electrons to tunnel out of the atom, the probability is typically extremely low for electrons to tunnel out of an atomic system in a solid. This is because the energy barriers imposed by the atomic potentials in solids are usually relatively high, and the wave functions of electrons are typically localized around the atomic nuclei. Therefore, the majority of electrons remain bound to their respective atoms within the solid.
However, quantum tunneling does have important implications in certain situations. For example, it plays a significant role in phenomena like electron transport in quantum devices, scanning tunneling microscopy, and tunneling spectroscopy.
In summary, while there is a non-zero probability for electrons to tunnel out of an atom in a solid according to quantum mechanics, the probability is typically very low due to the high energy barriers and the localized nature of electron wave functions within the solid.