Question

he potential energy between two atoms in a particular molecule has the form U(s) = 2.6/x^8 - 4.3/x^4 where the units of x are length and the numbers 2.G and 4.3 have appropriate units so that U(x) has units of energy. What b the equilibrium separation of the atoms (that is the distance at which the force between the atoms is zero)?

Answer 1

Answer:

x = 1.04866

Explanation:

Force can be defined from power energy by the expressions

          F = $- \frac{ dU}{ dx}$

in this case we are the expression of the potential energy

          U = $\frac{2.6}{x^{8} } - \frac{4.3}{ x^{4} }$

let's find the derivative

         dU / dx = 2.6 ( $\frac{-8}{x^{9} }$) - 4.3 ($\frac{-4}{ x^{5} }$)

         dU / dx = $- \frac{20.8}{ x^{9} } + \frac{17.2 }{ x^{5} }$

we substitute

          F = + \frac{20.8}{ x^{9} }  - \frac{17.2 }{ x^{5} }

at the equilibrium point the force is zero, so

           $\frac{20.8}{ x^{9} } = \frac{17.2}{ x^{5} }$

           20.8 / 17.2 = x⁴

            x⁴ = 1.2093

             x = $\sqrt[4]{ 1.2093}$

             x = 1.04866