Chapter 10, Problem 10.2PR

(a)

Interpretation Introduction

Interpretation:

The sketch which describes the form of potential energy and the distance at which potential energy is minimum has to be given if the repulsive term in the Lennard-Jones (12,6) –potential is replaced by an exponential form of ${\text{e}}^{-\text{r}/{\text{r}}_{\text{0}}}$.

Concept Introduction:

Lennard-Jones (12,6) –potential:

It is the model of the total potential energy between molecules.

The mathematical expression is given below:

  $\begin{array}{l}\text{V}\left(\text{r}\right)\text{=}\text{4}\text{ε}\left[{\left(\frac{{\text{r}}_{\text{0}}}{\text{r}}\right)}^{\text{12}}\text{-}{\left(\frac{{\text{r}}_{\text{0}}}{\text{r}}\right)}^{\text{6}}\right]\\ \\ {\text{r}}_{\text{0}}\text{-}\text{Separation}\text{at}\text{which}\text{V}\text{=}\text{0}\\ \text{ε}\text{-}\text{Depth}\text{of}\text{the}\text{well}\\ \text{r}\text{-}\text{Separation}\end{array}$

(b)

Interpretation Introduction

Interpretation:

The distance at which the expotential-6 potential is minimum has to be determined.

Concept Introduction:

Lennard-Jones (12,6) –potential:

It is the model of the total potential energy between molecules.

The mathematical expression is given below:

  $\begin{array}{l}\text{V}\left(\text{r}\right)\text{=}\text{4}\text{ε}\left[{\left(\frac{{\text{r}}_{\text{0}}}{\text{r}}\right)}^{\text{12}}\text{-}{\left(\frac{{\text{r}}_{\text{0}}}{\text{r}}\right)}^{\text{6}}\right]\\ \\ {\text{r}}_{\text{0}}\text{-}\text{Separation}\text{at}\text{which}\text{V}\text{=}\text{0}\\ \text{ε}\text{-}\text{Depth}\text{of}\text{the}\text{well}\\ \text{r}\text{-}\text{Separation}\end{array}$