Lennard Jones Potential

The Lennard-Jones 6-12 potential energy, which describes the potential energy between neutral gases, is \(u(r) = u_0(\frac{r_0}{r})^{12} - 2( \frac{r_0}{r})^6\), where \( r \) is the separation between atoms. For Ar, \( r_0 = 3.9 \times 10^{-10} \) m and \( u_0 = 1.6 \times 10^{-21} \) J (according to D. V. Schroeder, An Introduction to Thermal Physics).

Part 1

Roughly sketch the form of the potential energy as a function of \(r\). On your diagram indicate the value of \(r\) and \(u\) at the minimum energy in terms of \(r_0\) and \(u_0\) (note: \(\frac{du}{dr} = 0\) at this point). Also indicate where the potential energy starts to become positive, and its behavior as \(r\rightarrow{\infty}\).

upload your work as a png file named ‘\(\textbf{potential}\)’.

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Part 2

Derive an expression for the force between the atoms as a function of \(r\).

On your diagram from part 1 above, label the regions where the force is negative (attractive) between atoms, and where the force is positive (repulsive) between atoms.

For	Use
\(r_o\)	R
\(r\)	r
\(u_o\)	u

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Attribution

Problem is licensed under the CC-BY-NC-SA 4.0 license.