Question

Write the full ground-state electron configuration for each: (a) S (b) \(\mathrm{Kr}\) (c) Cs

Short answer

(a) 1s² 2s² 2p⁶ 3s² 3p⁴ (b) 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹⁰ 4p⁶ (c) 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹⁰ 4p⁶ 5s² 4d¹⁰ 5p⁶ 6s¹

Step-by-step solution

Understanding the Electron Configuration

Electron configuration describes the arrangement of electrons in an atom's orbitals. The order of filling orbitals follows the Aufbau principle, Pauli-exclusion principle, and Hund's rule.

Find the Atomic Number

Identify the atomic number of each element since it indicates the total number of electrons. For S (Sulfur): Atomic number is 16. For Kr (Krypton): Atomic number is 36. For Cs (Cesium): Atomic number is 55.

Sequence of Orbital Filling

Use the order of orbital filling: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s...

Write Electron Configuration for S (Sulfur)

Sulfur (atomic number 16): 1s² 2s² 2p⁶ 3s² 3p⁴

Write Electron Configuration for Kr (Krypton)

Krypton (atomic number 36): 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹⁰ 4p⁶

Write Electron Configuration for Cs (Cesium)

Cesium (atomic number 55): 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹⁰ 4p⁶ 5s² 4d¹⁰ 5p⁶ 6s¹

Key concepts

Aufbau principle

The Aufbau principle is fundamental for determining the electron configuration of an atom. It means 'building up' in German and reflects how electrons fill orbitals.
According to this principle, electrons occupy the lowest energy orbitals first. This process continues, with electrons filling up orbitals in a specific sequence until all electrons are placed.
This sequence can be remembered using the order: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s...
By following this order, we ensure that each electron is in its correct position, leading to the accurate electron configuration for each element.
This principle is illustrated in the given examples:

• For Sulfur, with atomic number 16, the electrons fill in the following order: 1s² 2s² 2p⁶ 3s² 3p⁴.
• For Krypton, with atomic number 36: 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹⁰ 4p⁶.
• And for Cesium, with atomic number 55: 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹⁰ 4p⁶ 5s² 4d¹⁰ 5p⁶ 6s¹.

By understanding the Aufbau principle, students can confidently determine how electrons are arranged in any atom's orbitals.

Pauli-exclusion principle

The Pauli-exclusion principle is another crucial concept for electron configuration. Proposed by Wolfgang Pauli, it states that no two electrons in an atom can have the same four quantum numbers.
This means that each electron in an atom must occupy a unique position in terms of its energy level and spin.
A single orbital can hold a maximum of two electrons, and these electrons must have opposite spins.
This principle ensures that electrons are distributed among the available orbitals appropriately and that each orbital reaches its maximum capacity of two electrons before moving to the next.
In our examples, we see this principle applied:

• For Sulfur, electrons are distributed across 1s, 2s, 2p, 3s, and 3p orbitals, with none of the electrons sharing the same state.
• For Krypton, which has more electrons, the configuration includes 4s, 3d, and 4p orbitals, each being maximized according to the Pauli-exclusion principle.
• And for Cesium, the 6s orbital is filled after all previous orbitals have been maximized with paired electrons.

Understanding the Pauli-exclusion principle helps students comprehend why atoms have their specific electron configuration and allows them to predict how electrons will fill up an atom's orbitals accurately.

Hund's rule

Hund's rule is the final essential principle for electron configuration. It focuses on how electrons populate orbitals of the same energy level.
According to Hund's rule, electrons will fill degenerate orbitals—those with the same energy—one at a time, with all electrons in these orbitals having parallel spins, before any pairing occurs.
This means that for orbitals like p, d, or f, which have multiple sub-levels, an electron will occupy each sub-level singly before pairing up.
This minimizes electron repulsion within the atom and is the most stable arrangement.
Dating back to the examples used:

• For Sulfur, the 3p orbitals have four electrons. According to Hund's rule, three of these electrons will occupy separate 3p orbitals first with parallel spins (3p³), and only the fourth electron will pair up (3p⁴).
• For Krypton, the 3d orbitals are filled first with all five electrons having parallel spins before any pairing occurs (3d¹⁰).
• And for Cesium, similar principles are applied throughout its more complex electron configuration.

By understanding Hund's rule, students can explain why, within an energy level, electrons fill up singly before pairing. This leads to a more stable and accurate electron configuration for atoms.