Question

Obtain the relation between the polarizability and the distance between two atoms for a two neutral atoms system.
(a) a=a/2


(b) a=a^3/2

(c) a= a^3

(d) a=a^3/2​

Answer 1

Answer:

a) a=a/2 is the right answer

Answer 2

Concept:

Polarizability often refers to a material's propensity to develop an electric dipole moment in proportion to an applied electric field.

Given:

A two neural atoms system.

Find:

The relation between the distance between the two atoms and the polarizability.

Solution:

Let the two atoms be A and B.

Let's assume two polarizable atoms at a distance 'a' with polarizability α.

The induced dipole moments be $\vec{p}_{A}$ and $\vec{p}_{B}$.

Therefore, the electric field of $\vec{p}_{A}$ at the position of  $\vec{p}_B$ is:

$E_A=\frac{p_A(3 [cos^2(\theta)-1])}{4\pi \varepsilon _0(a)^3}$

$E=\frac{p_A}{2\pi \varepsilon _0 a^3}$ when θ = 0

Now, The second dipole's induced dipole moment will have the following magnitude and be in the same direction as $p_A$:

$p_B=\alpha E_A$

$E_B=\frac{\alpha p_A}{(2\pi\varepsilon _0a^3)^2}$ is the field of this dipole at the position of the first dipole $p_A$.

Therefore, the induced dipole moment is:

$p_A=\alpha E_B=\frac{\alpha ^2p_A}{(2\pi\varepsilon _0a^3)^2}$

This will satisfy if $p_A=0$ or for any other $p_A$ if:

$a^6=\frac{\alpha ^2}{(2\pi\varepsilon _0)^2} \\a^6(2\pi\varepsilon _0)^2=\alpha ^2\\\alpha =a^3(2\pi\varepsilon _0)$

The relation between the polarizability and the distance between two atoms is $\alpha =a^3$.

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