# Attraction and repulsion of molecules of the same substance

My physics textbook says, "The amount of force by which molecules attract each other when they are moved away from each other by a certain distance, is lesser than the amount of force by which molecules repel each other when they are moved closer to each other by the same distance." Why?

• – Puk
Jul 4 at 6:31

I find that sentence very badly written, so I hope that your book isn't always like that. In any case, the potential describing the interaction between two molecules is probably of the form:

From this potential you can deduce the force: $$F=-\frac{dV}{dr}$$

Now look at the potential:

• When the molecules are closer, $$r$$ is shorter so $$V$$ has a steeper slope, so the force is stronger (also, since the slope is negative, the force is repulsive).
• When the molecules are further apart, $$r$$ is longer, $$V$$ is less steep so the force is less strong (and the force is attractive).

$$U=kQq/R$$ is Potential energy between two charges $$q$$ and $$Q$$ at distance $$R$$ so when $$R$$ tends to zero then $$U$$ tends to infinity and molecules always wants to be have high stability which comes from low potential energy so they repel strongly when they comes closer that's why "The amount of force by which molecules attract each other when they are moved away from each other by a certain distance, is lesser than the amount of force by which molecules repel each other when they are moved closer to each other by the same distance.