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nalin [4]
3 years ago
9

The potential energy between two atoms in a particular molecule has the form U(x) = 2.6 x8 − 5.1 x4 where the units of x are len

gth 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)?
Chemistry
1 answer:
nadezda [96]3 years ago
5 0

Explanation:

The given equation is as follows.

         U = \frac{2.6}{x^{8}} - \frac{5.1}{x^{4}}

or,  \frac{dU}{dx} = \frac{2.6 \times (-8)}{x^{9}} - \frac{5.1 \times (-4)}{x^{5}}

                    = \frac{-20.8}{x^{9}} + \frac{20.4}{x^{5}}

We know that for equilibrium, F = -\frac{dU}{dx} = 0

               \frac{dU}{dx} = 0

  \frac{-20.8}{x^{9}} + \frac{20.4}{x^{5}} = 0

     \frac{20.4}{x^{5}} = \frac{20.8}{x^{9}}

                     x = 1.004 m

                        = 1 m (approx)

Thus, we can conclude that the equilibrium separation of the given atoms is 1 m.

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