Which property of metals is better explained by band theory than by the sea-of-electrons model?

• A. The existence of semiconductors
• B. The malleability of metals
• C. The ability of metals to conduct heat
• D. The luster of metallic surfaces

Answer: (A)

Verified step by step guidance

1. Step 1: Understand the two models mentioned: the sea-of-electrons model and the band theory. The sea-of-electrons model treats valence electrons in metals as a 'sea' of free electrons that move around metal ions, explaining properties like malleability, conductivity, and luster.
2. Step 2: Recognize that the sea-of-electrons model is good at explaining general metallic properties such as malleability (how metals can be shaped), thermal conductivity, and the shiny appearance (luster) due to free electrons reflecting light.
3. Step 3: Introduce band theory, which describes the allowed energy levels of electrons in solids as continuous bands rather than discrete levels. This theory explains how electrons fill these bands and how the band structure determines electrical properties.
4. Step 4: Note that band theory is particularly useful for explaining the existence of semiconductors, where there is a band gap between the valence band and conduction band. This gap controls electrical conductivity, which the sea-of-electrons model cannot adequately describe.
5. Step 5: Conclude that the property better explained by band theory than by the sea-of-electrons model is the existence of semiconductors, because band theory accounts for the energy band structure and band gaps that govern semiconductor behavior.