Answer:
[tex]x\approx 0.948[/tex]
Explanation:
The correct formula for the potential energy between two atoms in a particular molecule is:
[tex]U(x) = \frac{2.1}{x^{8}}-\frac{5.2}{x^{4}}[/tex]
Where [tex]x[/tex] is the distance.
According to the definitions of potential energy and work, as well as the Work-Energy Theorem and the Principle of Energy Conservation. The relation between that and related force is:
[tex]F = -\frac{dU}{dx}[/tex]
The function is derived in terms of distance:
[tex]F (x) = \frac{84}{5\cdot x^{9}} -\frac{104}{5\cdot x^{5}}[/tex]
Then, it is needed to find at least of x so that F(x) equals to 0.
[tex]\frac{84}{5\cdot x^{9}}-\frac{104}{5\cdot x^{5}}=0[/tex]
[tex]\frac{84}{x^{4}}-104 = 0[/tex]
[tex]84-104\cdot x^{4} = 0[/tex]
[tex]x=\sqrt[4]{\frac{84}{104} }[/tex]
[tex]x\approx 0.948[/tex]
