question_answer

The potential energy of two atoms separated by a distance x is given by \[U=-A/{{x}^{6}}\], where A is a positive constant. What is the force exerted by one atom on another atom?

Answer:

                Here, \[U\,=-A/{{x}^{6}}\], F = ? From \[{{F}_{x}}=-\frac{d}{dx}\left( U \right)=-\frac{d}{dx}\left( \frac{-A}{{{x}^{6}}} \right)=A\left( \frac{-6}{{{x}^{7}}} \right)\] \[\therefore \]   force exerted by one atom on another atom = \[-6\,A/{{x}^{7}}\]