The correct statement(s) about intermolecular forces is(are)

To determine the correct statements about intermolecular forces, let us analyze each statement step-by-step:

1. Potential energy of point charges versus point charge-point dipole:
The potential energy between two point charges (ion-ion interaction) is inversely proportional to the distance $r$ between them:
$V_{\text{ion-ion}}\propto \frac{1}{r}$
The potential energy between a point charge and a point dipole (ion-dipole interaction) is inversely proportional to the square of the distance:
$V_{\text{ion-dipole}}\propto \frac{1}{r^2}$
As the distance $r$ approaches infinity ($r\to \infty$), the term $\frac{1}{r^2}$ approaches zero faster than $\frac{1}{r}$. Therefore, the ion-dipole potential energy approaches zero more rapidly than the ion-ion potential energy, making the first statement incorrect.

2. Average potential energy of two rotating polar molecules:
For stationary polar molecules, the dipole-dipole potential energy depends on $\frac{1}{r^3}$. However, when polar molecules are free to rotate, thermal motion averages the interaction. The resulting average potential energy (Keesom interaction) depends on the temperature $T$ and has a $\frac{1}{r^6}$ dependence:
$V_{\text{rotating dipole-dipole}}\propto \frac{1}{T{r}^6}$
Thus, the second statement is incorrect.

3. Temperature independence of dipole-induced dipole interaction:
A dipole-induced dipole interaction (Debye force) occurs when a polar molecule with a permanent dipole moment $\mu$ induces a temporary dipole in a neighboring nonpolar molecule with polarizability $\alpha$. The average interaction potential energy is given by:
$V_{\text{dipole-induced dipole}}=-\frac{2{\mu }^2\alpha }{{\left(4\pi {\epsilon }_0\right)}^2{r}^6}$
This equation does not contain temperature $T$. Therefore, the dipole-induced dipole average interaction energy is independent of temperature, making this statement correct.

4. Attraction between nonpolar molecules:
Even though nonpolar molecules lack permanent dipoles, continuous electron motion produces instantaneous dipoles at any given moment. These instantaneous dipoles induce temporary dipoles in adjacent molecules, creating an attractive force known as London dispersion force. Therefore, nonpolar molecules attract one another, making this statement correct.