What principle states that the maximum number of electrons in a shell is given by 2(n)^2?

The principle that states the maximum number of electrons in a shell is given by the formula 2(n)² is derived from the quantum mechanical model of the atom. This model describes how electrons are arranged in atomic orbitals and how their energies are quantized.

The formula indicates that for any given principal quantum number n, the maximum number of electrons that can occupy that energy level, or shell, is calculated by plugging n into the equation. For instance, when n = 1, the maximum is 2 electrons; when n = 2, it becomes 8 electrons; and so forth. This principle is crucial in chemistry and physics as it helps to explain the electron configuration of atoms and their chemical properties.

The Paul exclusion principle supports the idea that no two electrons in an atom can have the same set of quantum numbers, which inherently ties into the arrangement described by the formula 2(n)², ensuring that each energy level can accommodate a specific number of electrons without violating this fundamental rule. Therefore, this principle accurately captures how the arrangement of electrons behaves in quantized energy levels.