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Question

The potential energy is a function for the force between two atoms in a diatomic molecule is given by

`U(x)  = a/x^12 - b/x^6` where a and b are positive constants and x is the distance between the atoms . The position of stable equilibrium  for the system of the two atoms is given by


Options:
A .  `x = a/b`
B .  `x= sqrt(a/b)`
C .  `x= sqrt(3a)/b`
D .  `x=6sqrt((2a)/(b))`
Answer: Option D

`because       U(x) = a/x^12 - b/x^6`

At the stable equilibrium           ` (dU)/(Dx) = 0`

                                                   `- (12a)/(x^13) + (6b)/(x^7) = 0

                                          `x = ((2a)/(b))^(1/6)`



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