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

x = 1.04866

Step-by-step explanation:

Force can be defined from power energy by the expressions

F =
`- ( dU)/( dx)`

in this case we are the expression of the potential energy

U =
`(2.6)/(x^(8) ) - (4.3)/( x^(4) )`

let's find the derivative

dU / dx = 2.6 (
`(-8)/(x^(9) )`) - 4.3 (
`(-4)/( x^(5) )`)

dU / dx =
`- (20.8)/( x^(9) ) + (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

`(20.8)/( x^(9) ) = (17.2)/( x^(5) )`

20.8 / 17.2 = x⁴

x⁴ = 1.2093

x =
`\sqrt[4]{ 1.2093}`

x = 1.04866