Effect of number density on dielectric constant of a monoatomic gas Consider a monoatomic gas (e.g., a rare gas). If the number of atoms per unit volume changes, does its relative dielectric constant remain unchanged?

Introduction / Context:The macroscopic dielectric constant of a dilute gas arises from the microscopic electronic polarizability of its atoms and the number density. The Clausius–Mossotti (or Lorentz–Lorenz) relation connects these scales explicitly.

Given Data / Assumptions:

• Monoatomic, nonpolar gas with electronic polarizability α (approximately constant over modest ranges of density and weak fields).
• Low-density regime where local-field effects are handled by Lorentz–Lorenz correction.
• No ionization or chemical change.

Concept / Approach:The Lorentz–Lorenz relation for relative permittivity εr is: (εr − 1) / (εr + 2) = (N * α) / (3ε0) where N is number density. Therefore, εr depends directly on N; changing the number of atoms per unit volume changes εr. In the dilute limit (εr ≈ 1), one finds εr − 1 ≈ N * α / ε0, again showing proportionality to N.

Step-by-Step Solution:Write Lorentz–Lorenz relation with N explicit.Analyze small-contrast limit: εr ≈ 1 + (N α / ε0).Conclude: when N changes (e.g., by pressure variation), εr changes accordingly; it does not remain constant.

Verification / Alternative check:Refractive index n of gases satisfies (n^2 − 1)/(n^2 + 2) ∝ N; experimental measurements of n versus pressure confirm the dependence and hence the change in εr with N.

Why Other Options Are Wrong:Limiting to special temperatures or frequencies is unnecessary for this conclusion; the number-density dependence is general for nonresonant conditions.

Common Pitfalls:Assuming “intrinsic property” means unchanged by density; in gases, macroscopic εr is weakly above 1 and scales with N.

Final Answer:False