Understanding Gadolinium's Electron Configuration

Gadolinium (Gd) has an atomic number of 64, meaning it has 64 electrons. To determine its outer electron configuration, we follow the Aufbau principle, Hund's rule, and consider exceptions for stability.

Step 1: Write the Full Electron Configuration

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

For Gd (Z=64):

$1s^{2}2s^{2}2p^{6}3s^{2}3p^{6}4s^{2}3d^{10}4p^{6}5s^{2}4d^{10}5p^{6}6s^{2}4f^{7}5d^1$

Step 2: Identify the Outer Configuration

The outer electrons are those in the highest principal quantum number shells. For Gd, this is n=6 and n=5 (since 5d is higher energy than 4f but filled later). The outer configuration is typically written as the last filled orbitals: 4f, 5d, and 6s.

Step 3: Recognize the Exception

Gadolinium is an exception to the standard filling order. A half-filled f-subshell (4f⁷) provides extra stability. So, instead of 4f⁸ 5d⁰ 6s², it is 4f⁷ 5d¹ 6s².

Final Answer

The correct outer electron configuration for Gd is: $4f^{7}5d^{1}6s^2$

Related Topics

• Electron Configuration Rules
• Lanthanides and Their Exceptions
• Orbital Stability (Half-filled and Fully-filled Subshells)

Key Formulae and Theory

Aufbau Principle: Electrons fill orbitals from lowest to highest energy.

Hund's Rule: Orbitals are filled singly before pairing.

Exception for Stability: Half-filled (e.g., f⁷) or fully-filled subshells are more stable, leading to deviations in configuration.