The potential energy between two atoms in a molecule is given by, `U_((x))=(a)/x^(12)-(b)/x^(6)` , where a and b are positive constant and x is the distance between the atoms. The atoms is an stable equilibrium, when-

Options

A. x = 0
B. x = `(a)/(2b)`
C. `x = ((2a)/(b))^(1//6)`
D. x = `((11a)/(5b)) `

Explanation

(C )
Given that, `U(x) = (a)/(x^(12)) - (b)/(x^(6))`
We know `" " F = - (du)/(dx) `
`= (-12) a x^(-13) - (-6 b) x^(-7) = 0 `
or ` " " (6b)/(x^(7)) (12a)/(4 x^(13))`
or ` " " x^(6) = 12a//6b = 2a//b`
or `" " x = ((2a)/(b))^(1//6) `