DPST1031 Chap.2 Quantum Numbers and Electron Configurations
Quantum Numbers and Electron Configurations
Atomic orbitals emerge from the Schrödinger equation, and four quantum numbers describe every electron: n sets the level, l the subshell shape, the magnetic number the orientation and the fourth number the spin. This chapter shows how to test whether a set of quantum numbers is allowed, count orbitals and nodes, and build ground-state configurations by combining Hund's rule with the Aufbau and Pauli principles.
It covers spdf and arrows-in-boxes notation, the chromium and copper exceptions, transition-metal ions and paramagnetism. These skills sit in the second Threshold topic, so they are checked in the quiz and in In-term Test 1, and they return in the final whenever a question asks you to explain a periodic trend from a configuration.
What this chapter covers
- 01
Atomic orbitals and electron probability
- 02
The four quantum numbers and allowed values
- 03
Counting orbitals and nodes
- 04
Aufbau principle and filling order
- 05
Pauli exclusion principle
- 06
Hund's rule and arrows in boxes
- 07
Configurations of ions
- 08
Paramagnetic and diamagnetic species
Worked example · free
Box diagram and magnetism of an iron atom
- +1Iron has 26 electrons: 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d⁶, or [Ar] 4s² 3d⁶.
- +1Place the six 3d electrons: one in each of the five boxes with parallel spin, then the sixth pairs in the first box.
- +1That leaves four unpaired 3d electrons, so the iron atom is paramagnetic.
Key terms
- Atomic orbital
- A region around the nucleus described by its n, l and magnetic quantum numbers where an electron is likely to be found.
- Aufbau principle
- The rule that electrons occupy the lowest-energy available orbitals first.
- Pauli exclusion principle
- The rule that no two electrons in an atom share all four quantum numbers.
- Hund's rule
- The rule that electrons occupy equal-energy orbitals singly with parallel spins before pairing.
- Paramagnetic species
- A species with unpaired electrons that is attracted into a magnetic field.
- Radial node
- A spherical surface around the nucleus where the electron probability is zero.
- Noble-gas shorthand
- A configuration written as the preceding noble gas core plus the remaining electrons.
Quantum Numbers and Electron Configurations FAQ
Why does 4s fill before 3d but lose electrons first?
In a neutral atom the 4s orbital is lower in energy while it fills, because s electrons penetrate close to the nucleus. Once 3d electrons are present they shield and reorder the energies, so the 4s electrons become the outermost and are the first removed when a cation forms.
How many orbitals and electrons are in the n = 3 level?
Level 3 contains one 3s, three 3p and five 3d orbitals, nine in total. With two electrons per orbital it can hold eighteen electrons, which matches the general pattern of n² orbitals and 2n² electrons for a level.
Why are chromium and copper exceptions?
Chromium is [Ar] 4s¹ 3d⁵ and copper is [Ar] 4s¹ 3d¹⁰ because moving one 4s electron produces a half-filled or completely filled d subshell. Those arrangements have lower overall energy than the configuration predicted by the simple filling order.
What do orbital nodes tell me?
A node is a surface where the electron probability is zero. An orbital has n − 1 nodes in total: l angular nodes through the nucleus and n − l − 1 radial nodes around it. So a 3p orbital has one angular and one radial node, and a 1s orbital has none.
How many unpaired electrons does a carbon atom have?
Carbon is 1s² 2s² 2p². Its two 2p electrons occupy separate p orbitals with parallel spins, as Hund's rule requires, rather than pairing in one orbital. A ground-state carbon atom therefore has two unpaired electrons and is paramagnetic, which a box diagram shows at a glance.
Exam move
Write the quantum-number rules on one line and test yourself with ten random sets, deciding allowed or forbidden and giving the reason. Next, write configurations for every element from hydrogen to krypton in shorthand, marking chromium and copper. Then practise cations of the first transition series, removing 4s electrons first, and anions of the main groups.
For each species, draw only the partly filled subshell in boxes and count unpaired electrons, because that single drawing answers the configuration, Hund and paramagnetism questions together. Finally, practise explanation questions aloud: say why 4s empties before 3d, why Cr and Cu are exceptions, and why isoelectronic ions share a configuration. Each answer should name the principle being used in its first clause.
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