Question

Explain why the electron configuration for silver is \(1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 4 s^{2} 3 d^{10} 4 p^{6} 5 s^{1} 4 d^{10}\) rather than the predicted \(1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 4 s^{2} 3 d^{10} 4 p^{6} 5 s^{2} 4 d^{9}\).

Short answer

Silver prefers a full \(4d^{10}\) subshell for stability, resulting in \(5s^{1}\) instead of \(5s^{2}\).

Step-by-step solution

Understand Electron Configuration

Electron configuration is the arrangement of electrons in an atom. Electrons are filled in various atomic orbitals following specific rules—such as the Pauli exclusion principle, Hund's rule, and the Aufbau principle—which dictate the order in which orbitals are filled.

Analyze Aufbau Principle

The Aufbau principle suggests that electrons fill the lowest energy orbitals first. For silver (Ag), we would expect the electrons to fill up the 5s orbital before starting to fill the 4d orbital leading to the configuration predicted as \(1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 4 s^{2} 3 d^{10} 4 p^{6} 5 s^{2} 4 d^{9}\).

Identify Stability of Half-Filled and Fully Filled Subshells

A key aspect of electron configuration is the stability associated with half-filled and fully filled subshells. Subshells that are half-filled or fully filled have extra stability due to symmetrical distribution and exchange energy. This makes \(4d^{10}\) more stable than \(4d^{9}\).

Compare Energy Levels for 5s and 4d Orbitals

Though generally 5s orbitals are filled before 4d in the Aufbau principle order, for elements like silver, a full \(4d^{10}\) orbital is more stable than \(4d^{9}5s^{1}\). Consequently, one electron from \(5s\) moves into \(4d\) to minimize energy, slightly altering the standard order.

Conclude the Observed Electron Configuration

The electron configuration \(1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 4 s^{2} 3 d^{10} 4 p^{6} 5 s^{1} 4 d^{10}\) arises because of the enhanced stability associated with the full 4d subshell, contradicting the strict Aufbau filling order.

Key concepts

Aufbau principle

The Aufbau principle is a fundamental guideline in electron configuration. It states that electrons are filled into atomic orbitals starting from the lowest energy level. This is because electrons naturally seek the position of least energy available.

In practice, this principle involves following a specific order, beginning with the 1s orbital, followed by 2s, 2p, 3s, 3p, and so forth, filling up the energy levels sequentially. However, exceptions exist. In certain elements, like silver, the stability of electron configurations takes precedence, causing deviations from the predicted order.

Such exceptions occur due to the comparative energies between orbitals, as seen in the case of 4d and 5s orbitals in silver. The resulting stability of the filled or half-filled d subshells can lead to changes, where an electron will move to a lower energy configuration than what the basic Aufbau order predicts.

Subshell Stability

Subshell stability revolves around the concept that electron subshells reach a more stable, lower energy state when fully or half-filled. This stability arises due to a symmetrical arrangement of electrons and a phenomenon known as exchange energy, which provides additional stability through interactions among electrons.

Consider the case of silver. A fully filled 4d subshell (4d\(^{10}\)) is significantly more stable compared to a 4d\(^{9}\) subshell owing to these principles. The completed subshell is energetically favorable, leading silver to adopt an electron configuration that differs from the basic rules, with a full 4d subshell and just one electron in the 5s shell.

In essence, this emphasizes that the distribution of electrons is not solely dependent on the energy levels but also on achieving a state of maximal stability through fully utilized orbitals.

Pauli exclusion principle

The Pauli exclusion principle is a fundamental concept of quantum mechanics. It states that no two electrons can have the same set of quantum numbers within an atom. This is because each electron must have a unique state, specifically in terms of spin.

Quantum numbers describe different properties of electrons, with the fourth quantum number representing the electron spin, where each orbital holds only two electrons with opposite spins. This leads to a crucial consequence for electron configuration. Each electron will fit into the lowest possible energy state without duplicating the state of another electron already present in that orbital.

Due to the Pauli exclusion principle, while trying to place electrons into orbitals, this principle helps guide which orbitals can hold electrons and how those electrons will arrange themselves, ensuring every electron has its unique spin orientation. This contributes massively to determining electron configuration patterns.

Hund's rule

Hund's rule adds another layer to understanding electron configurations. It describes how electrons prefer to fill degenerate orbitals, which are orbitals at the same energy level, singly before any orbital gains a second electron.

This rule helps minimize electron-electron repulsions within an atom's orbitals. When electrons are placed in separate, equal-energy orbitals, they maintain parallel spins, which reduces the overall energy of the atom and increases stability.

For example, in the 4d subshell of silver, each orbital is first filled with one electron to reach five singly-occupied orbitals before any pairing occurs. Hund's rule ensures that within a given subshell, all degenerate orbitals achieve a state where repulsion is minimized, leading to a stable electron configuration before moving on to complete pairs.