Question

Van der Waals forces are weak attractive forces between molecules. At approximately what distance scale between molecules do these forces become significant?

Hint:

Van der Waals forces act only when molecules are separated by about a nanometre or less.

Answer 1

Van der Waals forces become significant at a distance scale of about \(10^{-9}\) metres, that is, around one nanometre.

Step 1: What van der Waals forces are.
These are weak, short range attractive forces that act between molecules due to temporary or induced fluctuations in their electron clouds, which create small, shifting dipoles.

Step 2: Why range matters.
Unlike gravity or electrostatic force, which can act over long distances, van der Waals forces fall off very rapidly with distance, roughly as the inverse sixth power of separation. This means they are only noticeable when molecules are extremely close to each other.

Step 3: The typical scale.
Molecules are usually separated by a fraction of a nanometre when these forces have a measurable effect, so the relevant distance scale is of the order of \(10^{-9}\) m, which is comparable to the size of a small molecule itself.

Step 4: Answer.
So van der Waals forces are important only at molecular separations of about \(10^{-9}\) m, and they weaken sharply if the molecules move even slightly farther apart.