IB Chemistry • Structure: Models of bonding and structure

Understand The Metallic Model — Understand Structure 2.3—The metallic model

Discover how a 'sea of electrons' explains the unique properties of metals.

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Inside this lesson 10 sections 5 questions 4 figures

SECTION 1

Historical Context & Motivation

Humans have worked with metals for thousands of years—from bronze weapons to gold jewelry—but it took centuries before scientists could explain why metals behave the way they do. Why does copper conduct electricity? Why can iron be hammered into sheets? Why do metals have that characteristic shine? Answering these questions required a model of bonding that was fundamentally different from the ionic and covalent models already in use.

1897 • Discovery of the Electron

J.J. Thomson discovered the electron using cathode ray tubes. This revealed that atoms contain negatively charged particles, setting the stage for understanding electrical conductivity in metals.

1900 • Drude's Free Electron Model

Paul Drude proposed the free electron model, treating valence electrons in a metal like a gas of free-moving particles. This early model successfully explained why metals conduct heat and electricity.

1927 • Quantum Mechanical Advances

Arnold Sommerfeld applied quantum mechanics to the free electron model, refining it by showing that electrons obey the Pauli exclusion principle and occupy energy bands rather than behaving like a classical gas.

1930s • Band Theory Emerges

Felix Bloch and others developed band theory, explaining how overlapping atomic orbitals create continuous energy bands. This theory unified the understanding of metals, semiconductors, and insulators.

The central question that drove all of this work was: if ionic compounds share electrons between specific atoms and covalent molecules share them in pairs, what kind of bonding holds a lump of metal together? The answer turned out to be something beautifully simple—electrons are shared, but by all the atoms at once. This idea became the metallic model of bonding.

SECTION 2

Core Principles of the Metallic Model

The metallic model describes how metal atoms bond together in a way that is completely different from ionic or covalent bonding. In a metal, atoms release their valence electrons into a shared pool. The result is a lattice of positively charged ions surrounded by freely moving electrons. Understanding this model requires grasping a few foundational ideas.

1

Delocalized Electrons

In a metallic bond, delocalized electrons are valence electrons that are not bound to any single atom. Instead, they move freely throughout the entire metallic structure, forming what is often called a 'sea of electrons.'
2

Cation Lattice

When metal atoms lose their valence electrons, they become positive ions (cations). These cations arrange themselves in a regular, repeating three-dimensional pattern called a lattice.
3

Electrostatic Attraction

The metallic bond is the electrostatic attraction between the positively charged cations in the lattice and the negatively charged sea of delocalized electrons. This attraction holds the metal together.
4

Non-Directional Bonding

Unlike covalent bonds, metallic bonds are non-directional. The electron sea surrounds every cation equally in all directions, which is why metal atoms can slide past each other without breaking the structure.
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KEY TAKEAWAY

Imagine a concert crowd where people (the cations) stand in neat rows while beach balls (the delocalized electrons) bounce freely over everyone's heads. No single person owns a beach ball—they all share them. The beach balls 'glue' the crowd together because everyone reaches up to touch them. That shared attraction is exactly how a metallic bond works: delocalized electrons hold the cation lattice together through electrostatic attraction.

SECTION 3

Visualizing the Metallic Model

The diagram below shows the metallic model in cross-section. Notice how the large, regularly spaced cations form a lattice, while small electrons drift freely between them. This arrangement is fundamentally different from ionic bonding, where electrons are transferred completely, or covalent bonding, where electrons are shared in localized pairs.

The Metallic Model: Sea of ElectronsM⁺M⁺M⁺M⁺M⁺M⁺M⁺M⁺M⁺M⁺M⁺= Metal cation (M⁺)= Delocalized electron (e⁻)= Electron sea (background)
The large violet spheres represent metal cations (M⁺) arranged in a regular lattice. The small cyan dots represent delocalized electrons that move freely between the cations. The pale blue background symbolizes the continuous 'sea' of shared electron density.

In the diagram, note two key features. First, the cations are evenly spaced—this reflects the ordered lattice structure of a real metal crystal. Second, the electrons are scattered randomly between the cations, illustrating that they belong to no particular atom. This delocalization is the defining feature of metallic bonding and is directly responsible for many of the properties we associate with metals, including electrical conductivity, thermal conductivity, malleability, and metallic lustre.

SECTION 4

How Metallic Bonding Explains Metal Properties

The metallic model is powerful because it explains a wide range of physical properties with a single, simple idea. Each property can be traced back to either the mobility of the delocalized electrons or the non-directional nature of the metallic bond. Let's examine the key properties one by one.

Electrical Conductivity

When a voltage is applied across a metal, the delocalized electrons drift toward the positive terminal. Because these electrons are free to move throughout the lattice, electric current flows easily. This is why metals are excellent electrical conductors. The more delocalized electrons a metal contributes per atom, the better it tends to conduct.

Thermal Conductivity

Delocalized electrons also carry kinetic energy. When one end of a metal bar is heated, the electrons in that region gain energy and move quickly through the lattice, transferring energy to cooler regions. This mechanism makes metals excellent thermal conductors. Lattice vibrations of the cations also contribute, but the electron mechanism is faster and dominant in metals.

Malleability and Ductility

When a metal is struck with a hammer, layers of cations slide over one another. In an ionic crystal, this would bring like charges together and the crystal would shatter. In a metal, however, the electron sea simply redistributes itself around the cations in their new positions. The non-directional metallic bond re-forms immediately, so the metal deforms without breaking. This is why metals are malleable (can be hammered into sheets) and ductile (can be drawn into wires).

Metallic Lustre

When light hits a metal surface, the delocalized electrons absorb the photon energy and then re-emit it in all directions. This gives metals their characteristic shiny appearance, known as metallic lustre. Because the electrons can respond to a wide range of wavelengths, most metals appear silvery-grey, though some (like copper and gold) selectively absorb certain wavelengths, giving them distinctive colors.

High Melting and Boiling Points

Breaking a metallic structure requires overcoming the strong electrostatic attraction between the cations and the electron sea. Metals with a higher charge on their cations or a smaller ionic radius have stronger metallic bonds, which leads to higher melting points. For example, sodium (Na) has a melting point of 98 °C, while iron (Fe) melts at 1538 °C—iron contributes more valence electrons and has a higher nuclear charge.

SECTION 5

Factors Affecting Metallic Bond Strength

Not all metals bond with the same strength. The strength of the metallic bond—and therefore properties like melting point—depends on two main factors: the charge of the cation (how many electrons each atom releases) and the ionic radius (how large the cation is). The diagram below illustrates how these factors influence bond strength.

Metallic Bond Strength vs. Cation Charge & SizeMelting points of selected metals across Periods 2 and 3Melting Point (°C)Metal Element0200400600800100098°CNa1+ charge660°CMg2+ charge660°CAl3+ charge181°CLi1+ (small)64°CK1+ (large)↑ Charge → ↑ Bond strength↑ Size → ↓ Bond strength
Across Period 3 (Na → Mg → Al), the increasing cation charge raises the melting point dramatically. Down Group 1 (Li → Na → K), the increasing ionic radius weakens the metallic bond and lowers the melting point. Both trends reflect changes in the electrostatic attraction between cations and delocalized electrons.

Two clear trends emerge from the data. Moving across a period (e.g., Na → Mg → Al), each successive element contributes more valence electrons to the sea and has a higher nuclear charge holding a smaller cation. This means the electrostatic attraction between the cations and the electron sea increases, producing stronger metallic bonds and higher melting points. Moving down a group (e.g., Li → Na → K), the ionic radius increases while the cation charge stays the same. The larger distance between the nucleus and the electron sea weakens the attraction, resulting in weaker metallic bonds and lower melting points.

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IB Exam Tip

When asked to explain trends in melting points of metals, always discuss both factors: the charge on the cation (number of delocalized electrons) and the ionic radius. Simply stating 'stronger metallic bonding' without explaining the underlying reason will not earn full marks.

SECTION 6

Worked Example: Comparing Metallic Bond Strength

Let's work through a typical IB-style question that asks you to use the metallic model to explain differences in physical properties.

Explain why magnesium has a higher melting point than sodium.

  1. 1

    Step 1 — Identify the electron configurations

    Sodium (Na) has the electron configuration [Ne] 3s1, so each Na atom contributes one valence electron to the sea. Magnesium (Mg) has the configuration [Ne] 3s2, contributing two valence electrons per atom.
    Na → Na⁺ + 1e⁻ ; Mg → Mg²⁺ + 2e⁻
  2. 2

    Step 2 — Compare cation charges

    Na forms a 1+ cation, while Mg forms a 2+ cation. The higher charge on Mg²⁺ creates a stronger electrostatic attraction with the delocalized electrons. Additionally, Mg contributes twice as many electrons to the sea, increasing the total negative charge density between the cations.
    Mg²⁺ has double the cation charge of Na⁺
  3. 3

    Step 3 — Compare ionic radii

    The Mg²⁺ ion is smaller than the Na⁺ ion because Mg has one more proton pulling the remaining electrons inward, and it has lost one more electron. A smaller cation means the electron sea is closer to the nucleus, further strengthening the electrostatic attraction.
    r(Mg²⁺) = 72 pm < r(Na⁺) = 102 pm
  4. 4

    Step 4 — State the conclusion

    Because Mg²⁺ has a higher charge and a smaller ionic radius than Na⁺, and because magnesium contributes more delocalized electrons per atom, the metallic bond in magnesium is significantly stronger than in sodium. More energy is required to overcome these stronger attractions, so magnesium has a higher melting point.
    Mg melting point (650 °C) >> Na melting point (98 °C)
ℹ

Model Answer Structure

For IB Chemistry, structure your answer in three parts: (1) state what each metal contributes (number of electrons and cation charge), (2) compare ionic radii, and (3) link these factors to the strength of electrostatic attraction and the resulting property difference. This pattern works for any comparison of metallic bond strength.

SECTION 7

Strengths and Limitations of the Metallic Model

Like all scientific models, the metallic model is a simplification. It does an excellent job explaining many everyday observations about metals, but it has blind spots. The table below summarizes what the model handles well and where it falls short.

AspectStrength of the ModelLimitation of the Model
ConductivityExplains why metals conduct electricity and heat via mobile electronsCannot quantitatively predict exact conductivity values
MalleabilityExplains why metals can be deformed—layers slide and bonds re-formDoes not explain why some metals are harder than others in detail
Melting pointsCorrectly predicts trends based on charge and ionic radiusFails to explain anomalies (e.g., why transition metals have very high melting points)
ColorQualitatively explains metallic lustre through photon re-emissionCannot explain why copper is reddish and gold is yellow (requires band theory)
AlloysExplains why metals can form alloys—different-sized atoms disrupt lattice regularityDoes not predict which elements will form stable alloys

Strengths and limitations of the metallic bonding model

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KEY TAKEAWAY

Think of the metallic model like a road map: it shows you the main highways and tells you how to get from city to city, but it doesn't show every side street or traffic light. For IB Chemistry, this 'road map' level of detail is exactly what you need—it explains the major trends and properties. More detailed models like band theory provide the side-street-level detail, but they're beyond the scope of this course.

SECTION 8

Connection to Band Theory and Advanced Models

The metallic model you've learned in this lesson is sometimes called the electron sea model. It works well for explaining general properties, but for questions like 'Why is copper colored but silver is not?' or 'Why do some metals become superconductors?', scientists need a more sophisticated framework called band theory.

FeatureElectron Sea Model (IB Level)Band Theory (Advanced)
Electron descriptionElectrons are delocalized and free to moveElectrons occupy continuous energy bands formed by overlapping atomic orbitals
ConductivityQualitative: 'electrons can move, so metals conduct'Quantitative: conduction depends on whether the valence band overlaps with the conduction band
Metals vs. insulatorsModel applies only to metalsExplains metals, semiconductors, and insulators using band gaps
Color of metalsCannot explain specific colorsExplains color based on which photon energies are absorbed during electron transitions between bands

Electron sea model vs. band theory

In band theory, when billions of metal atoms come together, their atomic orbitals merge into continuous energy bands. If the highest-energy occupied band (the valence band) overlaps with the next empty band (the conduction band), electrons can flow freely—this is what makes a material a metal. If there is a large gap between these bands, the material is an insulator. Semiconductors fall in between, with a small gap that can be overcome with heat or light. While you don't need to master band theory for IB Chemistry, knowing it exists helps you appreciate that the electron sea model is a stepping stone to deeper understanding.

SECTION 9

Practice Problems

Question 1: CONCEPTUAL

Describe the metallic bond in terms of the particles involved and the forces between them.
Show answer
A metallic bond is the electrostatic attraction between a lattice of positively charged metal cations and the surrounding sea of delocalized (free-moving) valence electrons. The metal atoms release their valence electrons, which are no longer associated with any single atom but move freely throughout the entire structure. The strong attraction between the positive cations and negative electron sea holds the metallic structure together.

Question 2: BASIC CALCULATION

Sodium (Na) has one valence electron and potassium (K) also has one valence electron. Both form 1+ cations. However, Na melts at 98 °C while K melts at 64 °C. Using the metallic model, explain this difference.
Show answer
Both Na and K have the same cation charge (1+), and both contribute one delocalized electron per atom. However, Na⁺ has a smaller ionic radius (102 pm) than K⁺ (138 pm) because potassium has an additional electron shell. In a smaller cation, the delocalized electrons are closer to the nucleus, so the electrostatic attraction between the cation and the electron sea is stronger. Stronger metallic bonds mean more energy is needed to separate the atoms, resulting in sodium's higher melting point.

Question 3: INTERMEDIATE

Explain why metals are malleable but ionic compounds are brittle, even though both involve electrostatic forces.
Show answer
In a metal, the bonding is non-directional—the delocalized electrons surround all cations equally. When a force is applied and layers of cations slide past one another, the electron sea redistributes itself around the new cation positions, and the metallic bond re-forms immediately. The structure deforms without breaking. In an ionic compound, however, ions are held in fixed positions. When layers shift, cations move next to cations and anions next to anions, producing strong repulsive forces between like charges. These repulsions cause the crystal to crack and shatter. The key difference is that metallic bonds are non-directional and can reform, while ionic bonds are position-dependent.

Question 4: APPLIED

Aluminium is used for overhead power cables despite being a weaker conductor than copper. Using the metallic model, explain (a) why aluminium conducts electricity well, and (b) suggest one reason related to its metallic bonding that makes it suitable for overhead cables.
Show answer
(a) Aluminium has the electron configuration [Ne] 3s²3p¹, so each atom contributes three valence electrons to the delocalized electron sea. When a potential difference is applied, these free electrons drift through the lattice, carrying charge and producing an electric current. With three delocalized electrons per atom, aluminium has a high density of mobile charge carriers, making it an excellent conductor. (b) Aluminium's relatively low density (2.70 g/cm³ compared to copper's 8.96 g/cm³) means that overhead cables weigh far less, reducing the load on support structures. At the bonding level, aluminium's cations are lighter (lower atomic mass), so for the same volume of metal, the overall mass is much lower while still maintaining strong metallic bonding and good conductivity.

Question 5: CRITICAL THINKING

Transition metals such as iron (Fe, melting point 1538 °C) have much higher melting points than main group metals like aluminium (Al, melting point 660 °C), even though both form 3+ cations. The simple electron sea model struggles to explain this. Suggest what additional factor(s) might account for the much stronger bonding in transition metals, and comment on whether this represents a limitation of the metallic model.
Show answer
The simple electron sea model considers only s-block valence electrons as being delocalized. However, in transition metals, d-electrons can also participate in metallic bonding. Iron, for example, can contribute some of its 3d electrons to the delocalized electron sea in addition to its 4s electrons. This increases both the number of delocalized electrons and the effective cation charge, dramatically strengthening the electrostatic attraction. Additionally, d-orbital overlap between adjacent atoms adds a directional component to the bonding that the simple electron sea model does not account for. This is indeed a limitation of the basic metallic model—it cannot fully explain the very high melting points and hardness of transition metals without invoking additional concepts from band theory or molecular orbital theory, where d-band contributions become crucial.

SUMMARY

Lesson Summary

Summary

The metallic model describes metals as a regular lattice of positive cations surrounded by a sea of delocalized electrons. The metallic bond is the electrostatic attraction between these cations and the mobile electrons. This model explains why metals have high electrical and thermal conductivity (free electrons carry charge and energy), why they are malleable and ductile (non-directional bonds re-form when layers slide), and why they exhibit metallic lustre (electrons re-emit absorbed light).

The strength of metallic bonding depends on two key factors: the charge of the cation (more valence electrons = higher charge = stronger attraction) and the ionic radius (smaller cation = closer electrons = stronger attraction). These factors explain why melting points increase across a period and decrease down a group. While the model has limitations—particularly for transition metals and for predicting exact values—it provides a robust framework for understanding and predicting the general properties of metallic substances at the IB level.

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