Figure 7.49 is a potential energy curve for the interaction of two neutral toms. The two-atom system is in a vibrational state indicated by the green horizontal line.

1. At , what are the approximate values of the kinetic energy K, the potential energy U, and the quantity K + U?
2. What minimum energy must be supplied to cause these two atoms to separate?
3. In some cases, when r is large, the interatomic potential energy can be expressed approximately as . For large r, what is the algebraic form of the magnitude of the force the two atoms exert on each other in this case?

The motion of electrons in a particular atom defines the potential and kinetic energy of the atom. And for two atoms, the potential energy depends on the distance between two atoms.

The total energy for the system is given by the sum of the potential energy and the kinetic energy. It is expressed as follows,

$E=K+U$ …(1)

Here, , K is the kinetic energy and U is the potential energy.

$F=\frac{dU}{dr}$ …(2)

Here, U is the potential energy and r is interatomic distance.

(a)From the given plot, the value of potential energy and the total energy corresponding to$r=r_1$ is as follows,

$U=-1.3 \text{eV}$

$E=-0.2 \text{eV}$

Substitute all the values in equation (1).

$$\begin{gathered} -0.2 \text{eV}=K+\left(-1.3 \text{eV}\right) \\ K=1.3 \text{eV}-0.2 \text{eV} \\ =1.1 \text{eV} \end{gathered}$$

Thus, the approximate values of the kinetic energy K is 1.1 eV, the potential energy U is -1.3 eV, and the quantity K + U is -0.2 eV.

(b)The required factor for determination of the minimum energy required to separate the two atoms is that the value of the interaction energy must be zero.

So, the required amount of energy that must be supplied is +0.2 eV to make the interaction energy zero. It can be expressed as follows,

$$\begin{gathered} E=-0.2 \text{eV +}-0.2 \text{eV} \\ =0 \end{gathered}$$

(c)Substitute all the values in equation (2) and solve the equation.

$$\begin{gathered} F=\frac{d}{dr}\left(\frac{-a}{r^6}\right) \\ =-\frac{6a}{r^7} \end{gathered}$$

Thus, theforce magnitude that is applied by two atoms on each other in the algebraic formis $-\frac{6a}{r^7}$.