A large number of free electrons exist in ______.

Question

Examoogle · Accepted Answer

Metals

Explanation: Metals have a large number of free electrons due to the overlapping of valence and conduction bands. These electrons are not bound to any specific atom and move freely throughout the crystal lattice, making metals excellent conductors of electricity.

Working Principle: In metals, the atomic orbitals of valence electrons overlap to form a continuous band structure called the conduction band. Because there is no energy gap (forbidden energy gap) between the valence band and the conduction band, thermal energy at room temperature is sufficient to excite electrons into the conduction band, facilitating high electrical conductivity.

Key Formulas: $J = \sigma E$ — Ohm's law in point form relating current density J, conductivity $\sigma$, and electric field E; $I = n A e v_d$ — Current equation where n is free electron density, A is cross-section, and $v_d$ is drift velocity

Key Points: Metals possess a high electron density (order of $10^{28} 	ext{ electrons/m}^3$); The Fermi level in metals lies within the conduction band; Conductivity in metals decreases with an increase in temperature due to increased lattice scattering; Semiconductors have a forbidden energy gap, preventing free flow of electrons at absolute zero

Advantages: High electrical and thermal conductivity; Good malleability and ductility for wiring

Disadvantages: Susceptible to oxidation and corrosion; Conductivity decreases as temperature rises

Applications: Electrical transmission cables; Electronic circuit interconnects; Heat sinks for cooling components

Additional Info: In insulators, the forbidden energy gap is typically greater than 5 eV, preventing conduction.. In semiconductors, the energy gap is relatively small (e.g., ~1.1 eV for Silicon at 300K).

Answer: B is correct — Metals exhibit a large number of free electrons due to the absence of a band gap and the overlapping of conduction and valence bands.

Exam Tip: Remember that while semiconductors become more conductive with heat, metals become less conductive due to increased electron-phonon scattering.

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