Lutetium (Lu) Revision Guide

Atomic Structure

Fundamental Particles

• Atomic Number (Z): 71
• Protons: 71 (in the nucleus)
• Electrons: 71 (in a neutral atom)
• Neutrons: The most abundant stable isotope is Lutetium-175 ($^{175}$Lu), which has 175 - 71 = 104 neutrons.
• Atomic Mass: 174.9668 u (for naturally occurring isotopic mixture).

Atomic Size

• Metallic Radius: 173.4 pm (picometers, for 12-coordination).
• Covalent Radius: Approximately 177 pm (calculated).
• Ionic Radius: For Lu³⁺, approximately 86.1 pm.

Electronic Configuration & Shell Diagram

Electronic Configuration

• Ground State Configuration: [Xe] 4f¹⁴ 5d¹ 6s²
• Condensed Notation: The [Xe] represents the configuration of Xenon (1s² 2s² 2p⁶ 3s² 3p⁶ 3d¹⁰ 4s² 4p⁶ 4d¹⁰ 5s² 5p⁶).
• Orbital Filling: Electrons first fill the 6s orbital, then the 4f orbital completely, and finally one electron enters the 5d orbital.

Shell Diagram Representation (Textual)

The distribution of electrons in different principal energy shells is as follows:

• K-shell (n=1): 2 electrons (1s²)
• L-shell (n=2): 8 electrons (2s² 2p⁶)
• M-shell (n=3): 18 electrons (3s² 3p⁶ 3d¹⁰)
• N-shell (n=4): 32 electrons (4s² 4p⁶ 4d¹⁰ 4f¹⁴)
• O-shell (n=5): 9 electrons (5s² 5p⁶ 5d¹)
• P-shell (n=6): 2 electrons (6s²)

Periodic Trends

Position in the Periodic Table

Lutetium (Lu) is the last element of the Lanthanide series, located in Period 6 and is often considered a d-block element due to its 5d¹ electron, although it is typically grouped with the f-block lanthanides.

Ionization Enthalpy

• First Ionization Enthalpy (IE₁): 523.5 kJ/mol (energy required to remove the first electron).
• Second Ionization Enthalpy (IE₂): 1340 kJ/mol (energy required to remove the second electron).
• Third Ionization Enthalpy (IE₃): 2022.3 kJ/mol (energy required to remove the third electron).
• Lutetium readily forms Lu³⁺ ions by losing its two 6s electrons and the single 5d electron, resulting in a stable [Xe] 4f¹⁴ configuration.

Electronegativity

• Pauling Scale Electronegativity: 1.27
• Lutetium has a relatively low electronegativity, characteristic of metals, indicating a tendency to lose electrons rather than attract them.

Electron Gain Enthalpy

• Electron Gain Enthalpy: Approximately +50 kJ/mol (estimated).
• Being a metal, Lutetium has a positive (or very slightly negative) electron gain enthalpy, meaning energy is generally required to add an electron to a neutral Lutetium atom.

Atomic Radius

• As part of the Lanthanide series, Lutetium exhibits the effect of Lanthanide Contraction. This phenomenon causes a gradual decrease in atomic and ionic radii across the lanthanide series, making Lutetium’s atomic radius smaller than expected based on its position in Group 3.

Key Physical Properties

• Standard State: Solid at 25 °C.
• Appearance: Silvery-white metal.
• Density: 9.84 g/cm³ (at 25 °C).
• Melting Point: 1663 °C (1936 K).
• Boiling Point: 3402 °C (3675 K).
• Oxidation State: The most common and stable oxidation state is +3.
• Magnetic Properties: Paramagnetic (due to unpaired electrons, though Lu³⁺ is diamagnetic as it has a filled 4f subshell). The element itself is paramagnetic.