Use our pauli exclusion calculator for quick and accurate calculations. Free online tool.
No two electrons can have the same set of quantum numbers
Maximum electrons per orbital: 2
The Pauli Exclusion Principle has a profound consequence: because no two electrons can share the same quantum state, electrons are forced to occupy progressively higher energy levels as more electrons are added to an atom. This is why atoms have distinct electron shell structures rather than all electrons collapsing into the lowest energy orbital. For helium (Z=2), both electrons fit in the 1s orbital with opposite spins, filling it completely. For lithium (Z=3), the third electron must begin a new shell at 2s, since the 1s orbital is already at capacity with its two electrons.
The exclusion principle applies not only to electrons but to all fermions — particles with half-integer spin such as protons and neutrons. It is the reason matter is stable: without this restriction, electrons in every atom would collapse into the lowest available orbital, and atoms as we know them could not exist. In chemistry, the Pauli Exclusion Principle combines with Hund's rule and the Aufbau principle to provide a complete set of rules for determining electron configurations, predicting orbital occupancy diagrams, and understanding paramagnetism and diamagnetism.
Our Pauli Exclusion calculator helps you determine, for any given set of quantum numbers, whether an electron configuration is allowed or forbidden by the exclusion principle. You can also use it to calculate the maximum number of electrons in a given orbital, subshell, or shell, and verify that proposed electron arrangements are physically valid. This is an indispensable tool for students of general chemistry, physical chemistry, and quantum mechanics.
Electron configuration, orbital diagrams, valence electrons, and electron arrangement
Explore CategoryThe Pauli Exclusion Principle states that no two electrons in the same atom can have identical values for all four quantum numbers (n, l, mₗ, mₛ), so each quantum state can be occupied by at most one electron.
An orbital is defined by a specific combination of n, l, and mₗ quantum numbers. Since the spin quantum number mₛ can only be +½ or −½, at most two electrons can differ in that remaining quantum number, giving each orbital a maximum occupancy of two.
Because electrons cannot share quantum states, they fill shells and subshells in a structured sequence. The number of elements in each period (2, 8, 8, 18, 18...) directly reflects the maximum electron capacity of the filling subshells imposed by the exclusion principle.
No — it applies to all fermions, which are particles with half-integer spin (1/2, 3/2, etc.), including protons, neutrons, and quarks. Bosons (integer spin) do not obey this restriction.
In orbital box notation, the exclusion principle requires that each box (orbital) contains at most two arrows (electrons), and those arrows must point in opposite directions, symbolizing the two allowed spin states +½ and −½.