Electronic polarizability vs. atomic size; constitutive relation for dilute gases Assertion (A): Electronic polarizability increases as atoms become larger. Reason (R): For rare gases, the relation ε0 (εr − 1) E = N αe E holds, where N is the number of atoms per m^3 and αe is the electronic polarizability.

Introduction / Context:
Electronic polarizability reflects how easily an electron cloud distorts under an applied electric field. It connects microscopic properties of atoms to macroscopic dielectric behavior, especially in dilute gases like the noble (rare) gases where only electronic polarization is significant.

Given Data / Assumptions:

• Dilute, noninteracting atomic gas (rare gases: He, Ne, Ar, etc.).
• Polarization P related to electric field E by P = ε0(εr − 1)E.
• Microscopic relation P = N αe E for electronic polarizability αe per atom.

Concept / Approach:

Larger atoms have more diffuse electron clouds farther from the nucleus, so a given field displaces charge more easily, increasing αe. In a dilute gas, the macroscopic polarization equals the sum of individual dipole moments per unit volume: P = N αe E. Equating with the macroscopic form shows εr − 1 = N αe / ε0, linking dielectric increment to αe and number density N.

Step-by-Step Solution:

Verification / Alternative check:

Trends across noble gases (He → Ne → Ar → Kr → Xe) show increasing polarizability with atomic size, consistent with the assertion and the relation.

Why Other Options Are Wrong:

Since both statements are true and the reason quantitatively connects εr to αe, options stating partial truth or incorrect explanation do not apply.

Common Pitfalls:

Confusing electronic polarizability (rapid, field-induced displacement) with orientational (dipolar) or ionic polarization; applying dense-medium corrections where local-field effects require Clausius–Mossotti—dilute-gas form suffices here.

Final Answer:

Both A and R are true and R is correct explanation of A