Summarizing the Pauli Exclusion Principle

The Pauli Exclusion Principle Summary

• The state of a system is completely described by a complete set of quantum numbers. This set is written as \((\mathrm{n, l,}\phantom{\rule{0.25em}{0ex}}{m}_{l},\phantom{\rule{0.25em}{0ex}}{m}_{s})\).
• The Pauli exclusion principle says that no two electrons can have the same set of quantum numbers; that is, no two electrons can be in the same state.
• This exclusion limits the number of electrons in atomic shells and subshells. Each value of \(n\) corresponds to a shell, and each value of \(l\) corresponds to a subshell.
• The maximum number of electrons that can be in a subshell is \(2(2l+1)\).
• The maximum number of electrons that can be in a shell is \(2{n}^{2}\).

Glossary

atomic number

the number of protons in the nucleus of an atom

Pauli exclusion principle

a principle that states that no two electrons can have the same set of quantum numbers; that is, no two electrons can be in the same state

shell

a probability cloud for electrons that has a single principal quantum number

subshell

the probability cloud for electrons that has a single angular momentum quantum number \(l\)