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

Question

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)

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3 years 2021-08-30T16:37:02+00:00 1 Answers 3 views 0

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