Elemental dielectrics — polarization model and absence of permanent dipoles Assertion (A): For an elemental dielectric, P = N a_e E_i, where N is atoms per m^3, P is polarization, a_e is electronic polarizability, and E_i is the internal electric field. Reason (R): In elemental dielectrics there are no permanent dipoles or ions.

Introduction / Context:
Elemental dielectrics (e.g., noble gases, nonpolar elemental solids) exhibit polarization primarily through distortion of electron clouds relative to nuclei when an electric field is applied. This is electronic polarization, which is linearly related to the internal field for small fields.

Given Data / Assumptions:

• No permanent molecular dipoles (nonpolar material).
• No ionic sublattices (elemental substance, not an ionic compound).
• Linear dielectric response at small fields.

Concept / Approach:
In the absence of orientational or ionic mechanisms, the polarization density reduces to P = N a_e E_i. The reason statement explains why only electronic polarizability appears: elemental dielectrics lack built-in dipole moments and mobile ions. Therefore, both statements are true and the reason correctly accounts for the assertion.

Step-by-Step Solution:
Write total polarizability as a = a_e for elemental dielectrics.Multiply by number density: P = N a E_i = N a_e E_i.Recognize that orientational (dipolar) and ionic contributions are absent by material class.Conclude the logical linkage: R explains A.

Verification / Alternative check:
Measured temperature independence of polarization in such materials supports the lack of orientational terms, consistent with P ∝ E_i through a_e.

Why Other Options Are Wrong:
Claiming R is false would contradict the definition of elemental, nonpolar dielectrics; denying the explanation ignores the mechanism simplification.

Common Pitfalls:
Confusing internal field E_i with applied field; mixing SI/cgs constants when comparing with Clausius–Mossotti formulas.

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