Electron Configurations and Orbital Diagrams电子排布式与轨道表示式

Big Idea · Structure and Properties (SAP)AP Science Practice 1 · Models and RepresentationsAP link · Unit 1~40 min

Learning goals

  • Use the aufbau principle to write full and noble-gas electron configurations for elements 1–36
  • Draw orbital diagrams using the Pauli exclusion principle and Hund's rule, and count unpaired electrons
  • Recognize chromium and copper as exceptions, and write configurations for common ions such as Fe²⁺ and Fe³⁺

Before you start

  • Orbitals and sublevels (2.2.4)

From 2, 8, 8, 1 to 1s²2s²2p⁶3s²3p⁶4s¹

In lesson 1.4.4 you could only say how many electrons each shell of the first 20 elements held: potassium was 2, 8, 8, 1. With sublevels and orbitals, you can say exactly which sublevel and which orbital every electron occupies. Placing electrons follows three rules.

The aufbau principle

In a ground-state atom, electrons occupy the lowest-energy sublevels available. The order of sublevel energies, from lowest to highest, is the aufbau principle构造原理 (from the German for “building up”):

1s→2s→2p→3s→3p→4s→3d→4p1s \to 2s \to 2p \to 3s \to 3p \to 4s \to 3d \to 4p →5s→4d→5p→6s→4f→5d→6p→⋯\to 5s \to 4d \to 5p \to 6s \to 4f \to 5d \to 6p \to \cdots

Notice the overlaps: 4s comes before 3d, 5s before 4d, and 6s before 4f and 5d. American textbooks often teach this order with a “diagonal rule” chart.

The Pauli exclusion principle and Hund’s rule

The Pauli exclusion principle泡利原理: an orbital holds at most 2 electrons, and they must have opposite spins, shown as ↑↓.

Hund’s rule洪特规则: when electrons enter a sublevel with several orbitals of equal energy, they spread out one per orbital, with parallel spins, before any orbital gets a second electron.

Electron configurations and orbital diagrams

An electron configuration lists the number of electrons in each sublevel, such as 1s²2s²2p³ for nitrogen. The inner part that matches a noble gas can be replaced by that noble gas’s symbol in brackets, giving noble-gas notation: sodium’s 1s²2s²2p⁶3s¹ becomes [Ne]3s¹.

An orbital diagram uses boxes for orbitals and arrows for electrons. Nitrogen’s three 2p electrons occupy separate orbitals with parallel spins, following Hund’s rule:

↑↓1s↑↓2s↑↓↑↓↑↓2p\underset{1s}{\boxed{\uparrow\downarrow}}\quad \underset{2s}{\boxed{\uparrow\downarrow}}\quad \underset{2p}{\boxed{\uparrow\phantom{\downarrow}}\boxed{\uparrow\phantom{\downarrow}}\boxed{\uparrow\phantom{\downarrow}}}

Oxygen has one more electron, which has to pair up with one of the 2p electrons:

↑↓1s↑↓2s↑↓↑↓↑↓2p\underset{1s}{\boxed{\uparrow\downarrow}}\quad \underset{2s}{\boxed{\uparrow\downarrow}}\quad \underset{2p}{\boxed{\uparrow\downarrow}\boxed{\uparrow\phantom{\downarrow}}\boxed{\uparrow\phantom{\downarrow}}}

Starting in period 4, there are two common ways to write the order. Iron is usually written in filling order in American textbooks, [Ar]4s²3d⁶. Chinese textbooks write sublevels in order of n, [Ar]3d⁶4s². Both describe the same arrangement, and AP accepts either.

Two exceptions: chromium and copper

The aufbau order predicts [Ar]4s²3d⁴ for chromium and [Ar]4s²3d⁹ for copper. Experiments show instead:

Cr:[Ar] 4s1 3d5\text{Cr}: [\text{Ar}]\,4s^1\,3d^5 Cu:[Ar] 4s1 3d10\text{Cu}: [\text{Ar}]\,4s^1\,3d^{10}

A sublevel that is exactly half-filled (such as d⁵) or completely filled (such as d¹⁰) is especially low in energy, so one 4s electron moves into 3d, half-filling it in chromium and filling it in copper.

Configurations of ions

Anions gain electrons in aufbau order: Cl⁻ is 1s²2s²2p⁶3s²3p⁶, the same as argon.

Cations lose electrons from the highest n first. Transition metals lose their 4s electrons before any 3d electrons, even though 4s filled first: Fe is [Ar]4s²3d⁶, Fe²⁺ is [Ar]3d⁶, and Fe³⁺ is [Ar]3d⁵.

Pick an element and click the boxes to build its orbital diagram. Try nitrogen, chromium, and copper:

Try it: choose an element and click the boxes to place electrons and build its orbital diagram

Sublevels are listed in filling order, lowest energy first. Click a box to cycle: ↑ → ↑↓ → ↓ → empty.

Example 1: Sulfur

Write the full and noble-gas electron configurations of a ground-state sulfur atom and the orbital diagram of its 3p sublevel. How many unpaired electrons does it have?

Step-by-step solution

  1. Count the electrons. Sulfur is element 16, so the atom has 16 electrons.

  2. Fill from lowest to highest energy. 1s takes 2, 2s takes 2, 2p takes 6, and 3s takes 2, for 12; the remaining 4 go into 3p:

    1s22s22p63s23p41s^2 2s^2 2p^6 3s^2 3p^4

    The first 10 electrons match neon, so the noble-gas form is [Ne]3s²3p⁴.

  3. Draw the 3p orbital diagram. Hund’s rule: electrons first occupy separate orbitals with parallel spins, and only after all three have one does the fourth pair up:

    ↑↓↑↓↑↓3p\underset{3p}{\boxed{\uparrow\downarrow}\boxed{\uparrow\phantom{\downarrow}}\boxed{\uparrow\phantom{\downarrow}}}

  4. Unpaired electrons. Two 3p orbitals hold just one electron: 2 unpaired electrons.

  5. A common mistake. Pairing up all four 3p electrons as “↑↓ ↑↓ empty,” which breaks Hund’s rule.

Example 2: Fe²⁺ and Fe³⁺

Write noble-gas configurations for Fe, Fe²⁺, and Fe³⁺. Why does Fe²⁺ tend to be oxidized to Fe³⁺ in air?

Step-by-step solution
  1. Fe. 26 electrons. [Ar] accounts for 18, leaving 8: 4s fills first (2), then 3d (6): [Ar]4s²3d⁶.
  2. Fe²⁺. A cation first loses the electrons with the highest n, the two 4s electrons (not the 3d electrons that were filled last): [Ar]3d⁶.
  3. Fe³⁺. It then loses one 3d electron: [Ar]3d⁵.
  4. Why Fe²⁺ is easily oxidized. Fe³⁺ has a half-filled 3d sublevel (one electron in each of the 5 orbitals), which is especially low in energy and stable, so Fe²⁺ readily gives up one more electron to become Fe³⁺.
  5. A common mistake. Writing Fe²⁺ as [Ar]4s²3d⁴, removing the 3d electrons first. 4s fills before 3d, but it also empties first.
Practice: is the arrangement correct? If not, which rule does it break?
  1. Carbon: 1s²2s²2p², with the two 2p electrons in separate orbitals with parallel spins
  2. Carbon: both 2p electrons squeezed into one orbital, two orbitals empty
  3. Sodium: 1s²2s²2p⁶3p¹
  4. A 1s box drawn with two up arrows, ↑↑
  5. Potassium: [Ar]3d¹
  6. Nitrogen: three 2p electrons in separate orbitals, drawn ↑, ↓, ↑
  7. Three electrons in the 2s sublevel
  8. Chromium: [Ar]4s¹3d⁵
  9. Oxygen: 1s²2s²2p⁴

Common mistakes

Mistake 1: “Fe²⁺ forms when iron loses two 3d electrons.” Cations lose the electrons with the highest n first, so Fe²⁺ loses its two 4s electrons: [Ar]3d⁶.

Mistake 2: “Since 3d is sometimes written before 4s, 3d fills first.” 4s fills first. Writing 3d before 4s, as Chinese textbooks do, just orders the sublevels by n. Don’t confuse the writing order with the filling order.

Mistake 3: “Chromium is [Ar]4s²3d⁴.” That’s the aufbau prediction; the real configuration is [Ar]4s¹3d⁵. Copper is also an exception: [Ar]4s¹3d¹⁰.

Quick check

What is the noble-gas configuration of a ground-state copper atom?

Which of these has 5 unpaired electrons?

Summary

  • Aufbau: 1s → 2s → 2p → 3s → 3p → 4s → 3d → 4p, with overlapping sublevels. Pauli: at most 2 electrons per orbital, with opposite spins. Hund: within a sublevel, spread out with parallel spins before pairing.
  • Configurations can be shortened with noble-gas notation, and orbital diagrams use boxes and arrows. Chromium ([Ar]4s¹3d⁵) and copper ([Ar]4s¹3d¹⁰) are exceptions: half-filled and filled d sublevels are especially stable.
  • Anions gain electrons in aufbau order; cations lose the highest-n electrons first, as in Fe²⁺ ([Ar]3d⁶) and Fe³⁺ ([Ar]3d⁵).
On to AP (for later)

AP topic 1.5 asks you to write electron configurations, including noble-gas notation, and topic 1.6 uses them to explain the number, position, and height of the peaks in a photoelectron spectrum. AP accepts either writing order. “Transition-metal ions lose their ns electrons first” is a favorite AP point: Fe²⁺ is [Ar]3d⁶, not [Ar]4s²3d⁴.

Practice this chapter: 2.2 · Atomic Structure · Basic, Medium, and Hard levels

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