The addition of a second electron to a single electron orbital can lead to a slight expansion of the orbital's volume due to electron-electron repulsions. This effect is known as electron-electron repulsion or electron-electron correlation.
Electron-electron repulsion arises from the negative charges of electrons. When two electrons occupy the same orbital, they have the same spin but must have opposite spin quantum numbers due to the Pauli exclusion principle. As a result, the two electrons in the same orbital experience electrostatic repulsion, as like charges repel each other.
This electron-electron repulsion causes the electron cloud associated with the orbital to spread out slightly, resulting in a larger spatial distribution or volume for the orbital. This effect is more pronounced in orbitals that are closer to the nucleus, such as the 1s orbital, where the electron-electron repulsion is stronger.
Therefore, when a second electron is added to an orbital, it tends to slightly expand in volume to accommodate the repulsion between the two electrons. This expansion helps to minimize the overall electrostatic repulsion between the electrons, leading to a more stable arrangement.
It's important to note that the expansion of the orbital is relatively small and the overall shape and characteristics of the orbital remain similar. The expansion is a consequence of the electron-electron repulsion and the need to distribute the negative charges more evenly within the orbital.