Quantum numbers and electron configuration explain where electrons are located in atoms and how they fill available orbitals. This cheat sheet helps students connect atomic structure, the periodic table, and chemical behavior. It is useful for writing configurations, drawing orbital diagrams, and predicting valence electrons.
These skills support later topics such as bonding, ions, and periodic trends.
The four quantum numbers are the principal quantum number , angular momentum quantum number , magnetic quantum number , and spin quantum number . Electron configurations follow the Aufbau principle, Pauli exclusion principle, and Hund's rule. Sublevels hold different maximum numbers of electrons: holds , holds , holds , and holds .
The periodic table can be used as a map for filling orbitals in the correct order.
Key Facts
- The principal quantum number identifies the main energy level, and allowed values are positive integers such as .
- The angular momentum quantum number identifies the sublevel, with for , for , for , and for .
- For a given sublevel, the magnetic quantum number can have values from to , including .
- The spin quantum number has only two allowed values, or .
- Each orbital can hold a maximum of electrons, and those electrons must have opposite spins according to the Pauli exclusion principle.
- A sublevel with quantum number contains orbitals and can hold a maximum of electrons.
- The Aufbau filling order begins , , , , , , , , , , , , , , , .
- Hund's rule says electrons occupy equal-energy orbitals singly with parallel spins before pairing begins.
Vocabulary
- Quantum number
- A number that describes a specific property of an electron in an atom, such as its energy level, sublevel, orbital, or spin.
- Orbital
- A region of space around the nucleus where an electron is likely to be found.
- Electron configuration
- A notation that shows how electrons are arranged among the energy levels and sublevels of an atom.
- Aufbau principle
- The rule that electrons fill the lowest available energy orbitals before occupying higher-energy orbitals.
- Pauli exclusion principle
- The rule that no two electrons in the same atom can have the same set of four quantum numbers.
- Hund's rule
- The rule that electrons fill orbitals of equal energy one at a time before pairing.
Common Mistakes to Avoid
- Filling before for neutral atoms is wrong because the Aufbau order places before .
- Putting two electrons in one orbital before each orbital has one electron is wrong because Hund's rule requires single occupancy first.
- Writing more than electrons in one orbital is wrong because the Pauli exclusion principle allows only two electrons with opposite spins.
- Using impossible quantum numbers such as when is wrong because can only range from to .
- Confusing valence electrons with all outer electrons in transition metals can be wrong because electrons may also affect bonding and ion formation.
Practice Questions
- 1 Write the full electron configuration for oxygen, which has atomic number .
- 2 How many orbitals are in a sublevel, and what is the maximum number of electrons it can hold?
- 3 Identify the element with the electron configuration .
- 4 Explain why the orbital diagram for nitrogen should show three unpaired electrons in the sublevel instead of one paired orbital and one single electron.
Understanding Quantum Numbers & Electron Configuration
An orbital is not a tiny circular track around the nucleus. It is a mathematical model that describes where an electron is likely to be found. An s orbital has a roughly spherical probability region.
A p sublevel contains three orbitals with different orientations in space. The d and f sublevels have more complex shapes.
These shapes matter because the outer orbitals are the regions that overlap when atoms form bonds. Electron configuration is therefore connected to the way substances react, not just to a memorized filling pattern.
The four quantum numbers work like a complete address for one electron in an atom. The first number gives the broad energy level. The second identifies the kind of sublevel and its general shape.
The third picks one orbital within that sublevel. The fourth distinguishes the two possible spin states. No two electrons in the same atom can have exactly the same complete address.
This limit explains why an orbital accepts only two electrons. In an orbital diagram, the box represents one orbital and arrows represent electrons. Opposite arrow directions show the required opposite spins when a box contains a pair.
Energy order needs careful attention because the number of an energy level does not always decide which sublevel fills first. For example, the four s sublevel is filled before the three d sublevel in many neutral atoms. This happens because sublevels have slightly different energies as electrons interact with the nucleus and with each other.
The usual filling order is an excellent starting model, but a few heavier elements do not match it perfectly. Chromium and copper are common examples.
Their electrons arrange in ways that create especially stable d sublevels. At school level, learn the standard order first, then treat these cases as specific exceptions rather than evidence that the whole rule fails.
The periodic table gives useful checks while writing a configuration. The wide middle section relates to d sublevels, while the detached rows relate to f sublevels. For main group elements, the electrons in the highest main energy level usually identify the valence electrons.
Those electrons strongly affect common ion charges and bonding patterns. When making a positive ion, remove electrons from the outermost main energy level first. For transition metals, this often means removing four s electrons before three d electrons, even though four s filled first.
Unpaired electrons provide another real result of orbital diagrams. Atoms with unpaired electrons are often attracted to a magnetic field. Draw diagrams slowly, fill single boxes before pairing, count every electron against the atomic number, and check that each arrow pattern follows the rules.