where the units of x are length and the numbers 2.6 and 5.1 have appropriate units so that U (x) has units of energy. What is the equilibrium separation of the atoms (that is the distance at which the force between the atoms is zero)

x = 1.00486 m

Explanation:

The complete question is:

" The potential energy between two atoms in a particular molecule has the form U (x) = (2.6) / x^8 - (5.1) / x^4 where the units of x are length and the num - bers 2.6 and 5.1 have appropriate units so that U (x) has units of energy. What is the equilibrium separation of the atoms (that is the distance at which the force between the atoms is zero) ? "

Solution:

- The correlation between force F and energy U is given as:

F = - dU / dx

F = - d[ (2.6) / x^8 - (5.1) / x^4] / dx

F = 20.8 / x^9 - 20.4 / x^5

- The equilibrium separation distance between atoms is given when Force F is zero:

0 = 20.8 / x^9 - 20.4 / x^5

0 = 20.8 - 20.4*x^4

x^4 = 20.8/20.4

x = (20.8/20.4) ^0.25

x = 1.00486 m