Electrons exhibit a property called spin, which is a fundamental property of particles in quantum mechanics. Spin can be thought of as the intrinsic angular momentum of an electron. It has two possible values: spin-up (+1/2) and spin-down (-1/2).
According to the Pauli exclusion principle, no two electrons within an atom can have the same set of quantum numbers, including their spin. This means that if one electron occupies a particular orbital around the nucleus with a specific spin, the other electron must have the opposite spin to occupy the same orbital.
When considering the attraction between electrons and a positively charged nucleus, it's important to note that electrons are negatively charged particles, and opposite charges attract. The positive charge of the nucleus attracts the negatively charged electrons, providing an electrostatic force that keeps the electrons in orbit around the nucleus.
The pairing of electrons with opposite spins is a result of the quantum mechanical nature of electrons and their behavior within atoms. It is a consequence of the Pauli exclusion principle, which ensures that no two electrons in an atom can have the same set of quantum numbers, including their spin. This principle helps to stabilize the electronic structure of atoms and allows for the formation of chemical bonds between atoms.