An electron cannot stay inside the nucleus of an atom because of the fundamental properties of matter and the principles of quantum mechanics.
In an atom, the nucleus contains positively charged protons and neutral or slightly negatively charged neutrons, while the negatively charged electrons orbit around the nucleus. The electrons are bound to the nucleus by the electromagnetic force, which is responsible for holding atoms together.
According to quantum mechanics, electrons occupy specific energy levels or orbitals around the nucleus. These energy levels determine the electron's position and energy within the atom. The lowest energy level is called the ground state, and electrons tend to occupy the lowest available energy levels before filling higher energy levels.
The Pauli exclusion principle states that no two electrons within an atom can have the same set of quantum numbers. This means that each energy level can only accommodate a specific number of electrons with different quantum states. The maximum number of electrons that can occupy the innermost energy level is two, and the subsequent energy levels have increasing capacity.
In addition to the Pauli exclusion principle, there is a concept known as the Heisenberg uncertainty principle. It states that it is impossible to simultaneously know the exact position and momentum of a particle with absolute certainty. This principle applies to electrons as well. The more precisely we try to measure the position of an electron, the less precisely we can determine its momentum, and vice versa.
Considering these principles, if an electron were to enter the nucleus, it would violate both the Pauli exclusion principle and the Heisenberg uncertainty principle. The electron's position and momentum would become uncertain, making it impossible to define its behavior accurately. Therefore, electrons cannot exist inside the nucleus but instead occupy specific energy levels around it.