# 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 â€˜$$\textbf{potential}$$â€™.

File upload will appear here

## 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