Explanation
1. Given Data
2. The Clausius-Mossotti Relation
The Clausius-Mossotti relation connects the macroscopic property of a dielectric material (its relative permittivity εr) with the microscopic property of its constituent atoms or molecules (its molecular polarizability α).
The standard mathematical equation is given by:
εr+2εr−1=3ε0Nα
Where:
εr is the relative permittivity.
N is the number of atoms/molecules per unit volume (number density).
α is the electronic/molecular polarizability.
ε0 is the permittivity of free space.
3. Step-by-Step Calculation
We need to evaluate the directly requested expression 3ε0Nα. By rearranging the Clausius-Mossotti formula, we see it is directly equal to the left-hand side expression:
3ε0Nα=εr+2εr−1
Substitute the given value εr=4 into the formula:
3ε0Nα=4+24−1
3ε0Nα=63
3ε0Nα=21
Correct Answer
The correct option is (a) 21.
