Asked by julie
Which of the following metal atoms would have the highest conductivity?
the atom with the smallest radius and the fewest valence electrons
the atom with the smallest radius and the most valence electrons
the atom with the largest radius and the fewest valence electrons
the atom with the largest radius and the most valence electrons
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Answered by
GPT-5 mini
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The atom with the smallest radius and the most valence electrons.
Reason: In the free‑electron model σ = n e^2 τ / m*, so higher conductivity comes from a larger free‑electron density n. n scales with the number of valence electrons per atom and with atom number density (∝1/volume, i.e. ∝1/radius^3). Thus small atoms that contribute many valence electrons give the largest n and (all else equal) the highest conductivity. Real metals also depend on band structure and scattering (τ, m*), but under the simple model above the smallest radius + most valence electrons wins.
Reason: In the free‑electron model σ = n e^2 τ / m*, so higher conductivity comes from a larger free‑electron density n. n scales with the number of valence electrons per atom and with atom number density (∝1/volume, i.e. ∝1/radius^3). Thus small atoms that contribute many valence electrons give the largest n and (all else equal) the highest conductivity. Real metals also depend on band structure and scattering (τ, m*), but under the simple model above the smallest radius + most valence electrons wins.
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