pauli exclusion principle and explanation
Pauli’s Exclusion Principle:
In 1925, physicist W. Pauli proposed a principle regarding the position and distribution of electrons in different energy levels of an atom, which is recognized as Pauli’s Exclusion Principle.
“No two electrons in an atom can have the same set of four quantum numbers. In other words, even if the maximum of three quantum numbers are identical for two electrons in a given atom, the fourth quantum number must be different.”
For instance, a Helium (He) atom contains 2 electrons in its 1s orbital. Although the first three quantum numbers for these two electrons are identical, the fourth quantum number—namely the spin quantum number—is different. For example:
It is evident from the sets of four quantum numbers for the two electrons shown above that while the first three quantum numbers are identical, the fourth one is different. This is because for two electrons to occupy the same orbital, they must rotate in opposite spins to remain under mutual attraction, acting like two opposite magnetic poles. For this reason, even though the three quantum numbers n, l, and m are identical for the He atom, the value of the fourth quantum number, i.e., spin (s), must be different, which validates Pauli’s Exclusion Principle.
Determination of Quantum Number Sets for Different Electrons:
The orbital configuration using the box method for an Oxygen (8O) atom and the precise chart of quantum numbers for each specific electron are provided below:
| Electron | Orbital | n | l | m | s |
|---|---|---|---|---|---|
| For 1st electron | 1s | 1 | 0 | 0 | + ½ |
| For 2nd electron | 1s | 1 | 0 | 0 | – ½ |
| For 3rd electron | 2s | 2 | 0 | 0 | + ½ |
| For 4th electron | 2s | 2 | 0 | 0 | – ½ |
| For 5th electron | 2px | 2 | 1 | -1 | + ½ |
| For 6th electron | 2py | 2 | 1 | 0 | + ½ |
| For 7th electron | 2pz | 2 | 1 | +1 | + ½ |
| For 8th electron | 2px | 2 | 1 | -1 | – ½ |
Pauli’s Exclusion Principle — Questions and Answers
Question: State Pauli’s Exclusion Principle.
Answer: No two electrons in a particular atom can have the same set of four quantum numbers (n, l, m, s). Even if the values of three quantum numbers are identical, the value of the fourth quantum number must be different.
Question 1: Explain Pauli’s Exclusion Principle with respect to a Helium (2He) atom.
• For 2nd electron: n = 1, l = 0, m = 0, s = – ½
Question 2: “An orbital cannot accommodate more than two electrons” — Explain in light of Pauli’s principle.
Answer: According to Pauli’s principle, no two electrons in the same atom can have an identical set of four quantum numbers. For a specific orbital, the first three quantum numbers (n, l, m) remain fixed or constant. Only the fourth quantum number, i.e., the spin quantum number (s), can have two distinct values (+ ½ and – ½). If a third electron attempts to enter that same orbital, its spin value would inevitably match one of the existing two electrons, which violates Pauli’s principle. Therefore, an orbital can accommodate a maximum of two electrons with opposite spins.
Question 3: Why is Pauli’s Exclusion Principle called an ‘Exclusion’ principle?
Answer: According to Pauli’s principle, even if the first three quantum numbers of two electrons in a specific orbital are identical, their spins or directions of rotation must be opposite. This implies that if an orbital is already completely filled with two electrons having opposite spins, a third electron cannot enter with that same set of quantum numbers. In other words, the door to that orbital becomes closed or ‘excluded’ for any new electron. Because this rule excludes or bars other electrons from sharing the exact same quantum state, it is called the ‘Exclusion Principle’.
Question 4: Explain the quantum number set of the 8th electron of Oxygen in light of Pauli’s principle.
• Set for the 8th electron: n = 2, l = 1, m = -1, s = – ½
