Match the type of interaction in column A with the distance dependence of their interaction energy in column B:
A                                               B
(i) ion - ion                        (a) $$\frac{1}{r}$$
(ii) Dipole - dipole         (b) $$\frac{1}{r^2}$$
(iii) London dispersion  (c) $$\frac{1}{r^3}$$
                                          (iv) $$\frac{1}{r^6}$$

We begin by recalling the general form of the potential (interaction) energy for the three kinds of intermolecular or inter-ionic forces given in the question.

For two oppositely or similarly charged ions (ion-ion interaction), Coulomb’s law tells us that the potential energy $$E$$ varies inversely with the separation $$r$$ between their centres. Stated mathematically, the law is

$$E \;=\; \dfrac{kq_1q_2}{r},$$

where $$k$$ is Coulomb’s constant and $$q_1, q_2$$ are the ionic charges. The key point for matching is the $$\dfrac{1}{r}$$ dependence.

Next, for two permanent electric dipoles (dipole-dipole interaction) the classical electrostatic derivation gives

$$E \;=\; -\,\dfrac{\mu_1\mu_2}{4\pi\varepsilon_0\,r^{3}},$$

where $$\mu_1, \mu_2$$ are the dipole moments. Here we clearly see the $$\dfrac{1}{r^{3}}$$ dependence.

Finally, London dispersion forces (also called induced-dipole-induced-dipole forces) arise from correlated instantaneous charge fluctuations. Quantum-mechanical treatment leads to the well-known expression

$$E \;=\; -\,\dfrac{C_6}{r^{6}},$$

where $$C_6$$ is a constant characteristic of the interacting species. Thus the dependence is $$\dfrac{1}{r^{6}}$$.

Let us now compare these powers of $$r$$ with the entries listed in column B.

We have

$$\dfrac{1}{r}\;=\;(a), \qquad \dfrac{1}{r^{2}}\;=\;(b), \qquad \dfrac{1}{r^{3}}\;=\;(c), \qquad \dfrac{1}{r^{6}}\;=\;(d).$$

Substituting the results obtained above:

• Ion-ion corresponds to $$\dfrac{1}{r} \;\Rightarrow\; (a).$$

• Dipole-dipole corresponds to $$\dfrac{1}{r^{3}} \;\Rightarrow\; (c).$$

• London dispersion corresponds to $$\dfrac{1}{r^{6}} \;\Rightarrow\; (d).$$

Putting these matches together, we get

$$(i)\!-\!(a),\; (ii)\!-\!(c),\; (iii)\!-\!(d).$$

Looking at the four options supplied, this exact sequence appears only in Option D.

Hence, the correct answer is Option D.