In a molecule, the potential energy between two atoms is given by U(x)=(a)/(x^(12))-(b)/(x^(6)). Where a and b are positive constants and x is the distance between atoms. Find the value of x at which force is zero and minimum P.E. at that point.

In a molecule, the potential energy between two atoms is given by U(x)

1.	In a molecule, the potential energy between two atoms is given by U(x)=(a)/(x^(12))-(b)/(x^(6)). Where a and b are positive constants and x is the distance between atoms. Find the value of x at which force is zero and minimum P.E. at that point.
Answer» SOLUTION :Force is ZERO `rArr (dU)/(dx) = 0` i.e., `a (-12) x^(-13) - b(-6) x^(-7)= 0` `(-12a)/(x^(13))+(6b)/(x^(7))=0rArr(12a)/(x^(13))=(6b)/(x^(7))` `rArrx^(6)=(2A)/(b)thereforex=[(2a)/(b)]^(1//6)` `U_(min)=a((b)/(2a))^(12//6)-b((b)/(2a))^(6//6)` `rArr U_(min)=(AB^(2))/(4a^(2))-(b^(2))/(2a)rArrU_(min)=(-b^(2))/(4a)`