If the potential energy of a gas molecule is U= M/(r^6) - N/(r^12) M and N being positive constants, then the potential energy at equilibrium must be

If the potential energy of a gas molecule is U= M/(r^6) - N/(r^12) M a

1.	If the potential energy of a gas molecule is U= M/(r^6) - N/(r^12) M and N being positive constants, then the potential energy at equilibrium must be
Answer» ZERO `(M^2)/(4N)` `(N^2)/(4M)` `(MN^2)/(4)` Solution :`F = (-(DU))/(dr) = -(d)/(dr) [(M)/(R^6) - N/(r^(12))] = - [(-6M)/(r^7)+ (12N)/(r^(13))]` In equilibrium POSITION , `F = 0` `:. (6M)/(r^7) - (12N)/(r^13) = 0 " or " r^6 = (2N)/(M)` `:.` Potential energy at equilibrium position `U = M/((2N//M)) - N/((2N//M)^2) = (M^2)/(2N) - (M^2)/(4N) = (M^2)/(4N)`