There are fewer electrons in orbitals closer to an atom's nucleus due to the fundamental principles of quantum mechanics and the electronic structure of atoms. This behavior is governed by the Pauli exclusion principle and the concept of electron energy levels.
According to the Pauli exclusion principle, no two electrons within an atom can have the same set of quantum numbers. These quantum numbers include the principal quantum number (n), the azimuthal quantum number (l), the magnetic quantum number (m), and the spin quantum number (s).
The principal quantum number (n) determines the energy level or shell of an electron. The higher the value of n, the farther the electron is from the nucleus and the higher its energy. Each shell can accommodate a specific maximum number of electrons. The maximum number of electrons that can be accommodated in a given shell is given by the formula 2n^2.
Furthermore, the electrons in an atom occupy orbitals, which are regions of space with specific shapes and orientations. Each orbital can hold a maximum of two electrons, with opposite spins.
In an atom, electrons fill the available orbitals starting from the lowest energy level (n = 1) and moving progressively to higher energy levels. This is known as the Aufbau principle. As electrons are added to higher energy levels, they occupy orbitals farther away from the nucleus.
The distribution of electrons in atoms is governed by the principle of filling orbitals in a way that minimizes electron-electron repulsion. Electrons occupy orbitals in a way that maximizes their separation, resulting in a more stable electronic configuration.
Therefore, there are fewer electrons in orbitals closer to the nucleus because those orbitals have lower energy levels and are filled before the higher energy orbitals. This arrangement ensures that the electrons occupy the available orbitals in a manner that maximizes stability and minimizes electron-electron repulsion.