Clausius–Mossotti style plot — temperature-independent intercept Assertion (A): In the standard plot, the y-intercept equals N(a_e + a_i), where N is the number of atoms per m^3, a_e is electronic polarizability, and a_i is ionic polarizability. Reason (R): a_e and a_i are independent of temperature.

Introduction / Context:
For dielectrics without orientation polarization, the Clausius–Mossotti type relationship separates temperature-independent (electronic and ionic) polarizabilities from temperature-dependent orientational effects. When one plots an appropriate function of permittivity against 1/T for a polar material, the intercept is governed by the temperature-invariant polarizabilities.

Given Data / Assumptions:

• N is atomic number density (atoms per m^3).
• a_e: electronic polarizability; a_i: ionic polarizability.
• Electronic and ionic responses are assumed insensitive to moderate temperature changes compared with orientational effects.
• Linear small-field behavior is assumed.

Concept / Approach:
The total polarizability per atom is a = a_e + a_i + a_o(T). In many treatments, the plotted relation has a temperature-dependent term stemming from orientation polarization a_o ∝ 1/T, and a temperature-independent intercept from a_e + a_i. Hence, the intercept is proportional to N(a_e + a_i). R explains why that intercept is constant with temperature: a_e and a_i are essentially temperature-independent over the range of interest.

Step-by-Step Solution:
Recognize that a_e and a_i do not vary significantly with T.Orientation polarization contributes a term ∝ 1/T to the dependent variable.Thus, extrapolation to 1/T → 0 yields the intercept ∝ N(a_e + a_i).Therefore both A and R are true, and R explains A.

Verification / Alternative check:
Standard derivations show slope ∝ dipole moment squared and intercept ∝ sum of electronic and ionic polarizabilities.

Why Other Options Are Wrong:
Denying either statement contradicts classical dielectric theory used in solid-state physics and materials science.

Common Pitfalls:
Forgetting the necessary proportionality constants; mixing SI and cgs notations; assuming electronic polarizability varies strongly with T.

Final Answer:
Both A and R are true and R is correct explanation of A