Chapter 3.5, Problem 70E

Solution

a.

To graph: Graph the potential energy $E$ (the energy stored for use at a later time) between two ions in a certain molecular structure is modeled by the function $E=–\frac{5.6}{r}+10e^{–\frac{r}{3}}$ , where $r$ is the distance separating the nuclei.

Given information: The function of potential energy $E$ is $E=–\frac{5.6}{r}+10e^{–\frac{r}{3}}$ .

Graph:

The function of potential energy: $E=–\frac{5.6}{r}+10e^{–\frac{r}{3}}$

Graph this function in the window $\left[–\text{1}0,\text{1}0\right]$ by $\left[–\text{1}0,\text{3}0\right]$ ;

  

Interpretation:

Graph the function as indicated. Given that $r$ is a distance between two objects, it makes no sense for $r$ to be negative. Thus the graph shown in quadrant II is not representative of the situation.

b.

To graph: Graph the potential energy $E$ (the energy stored for use at a later time) between two ions in a certain molecular structure is modeled by the function $E=–\frac{5.6}{r}+10e^{–\frac{r}{3}}$ , where $r$ is the distance separating the nuclei.

Given information: The function of potential energy $E$ is $E=–\frac{5.6}{r}+10e^{–\frac{r}{3}}$ .

Graph:

The function of potential energy: $E=–\frac{5.6}{r}+10e^{–\frac{r}{3}}$

The domain of this function is $r>0$ ,

Graph this function in the window $\left[0,10\right]$ by $\left[–\text{1}0,5\right]$ ;

  

Interpretation:

The maximum potential energy is $\text{2}.\text{381}$ (no unit given).