Quantum numbers are the address system for electrons in atoms. They describe an electron's energy level, orbital shape, orbital orientation, and spin. This matters because electron arrangement controls bonding, periodic trends, spectra, and chemical reactivity.
Instead of imagining electrons as tiny planets, quantum numbers help describe where electrons are likely to be found.
Key Facts
- Principal quantum number: n = 1, 2, 3, ... and it describes the main energy level and approximate orbital size.
- Angular momentum quantum number: l = 0 to n - 1 and it describes orbital shape.
- Subshell letters match l values: l = 0 is s, l = 1 is p, l = 2 is d, l = 3 is f.
- Magnetic quantum number: ml = -l to +l, including 0, and it describes orbital orientation in space.
- Spin quantum number: ms = +1/2 or -1/2 and it describes the two allowed electron spin states.
- An orbital is defined by n, l, and ml, while a specific electron in that orbital is fully described by n, l, ml, and ms.
Vocabulary
- Quantum number
- A number that describes a permitted property of an electron in an atom.
- Orbital
- A region of space around the nucleus where an electron is likely to be found.
- Subshell
- A group of orbitals within the same main energy level that have the same shape type.
- Electron spin
- A quantum property of an electron that can have one of two allowed values, +1/2 or -1/2.
- Pauli exclusion principle
- The rule that no two electrons in the same atom can have the exact same set of four quantum numbers.
Common Mistakes to Avoid
- Using l = n is wrong because l can only range from 0 to n - 1 for a given energy level.
- Counting ml values incorrectly is wrong because ml includes every integer from -l to +l, including 0, so the number of orbitals is 2l + 1.
- Saying n determines orbital shape is wrong because n mainly describes energy level and size, while l determines shape.
- Giving two electrons in one orbital the same ms value is wrong because paired electrons in the same orbital must have opposite spins.
Practice Questions
- 1 For n = 3, list all allowed l values and identify the corresponding subshell letters.
- 2 For a d subshell, find l, list all possible ml values, and calculate the number of orbitals.
- 3 Explain why the quantum numbers n = 2, l = 2, ml = 0, ms = +1/2 are not allowed for an electron in an atom.