Question

The graph in Fig.16.56 shows the electric potential energy for a system of two interacting objects, as a function of the distance between the objects. What system might this graph represent?

(1) Two Protons, (2) Two sodium ions, (3) Two neutrons, (4) Two chloride ions, (5) Two electrons, (6) A Proton and an Electron, (7) A sodium ion and a chloride ion.

Short answer

The above graph represents Two Protons, Two Sodium ions, Two neutrons, Two chloride ions, Two electrons

Step-by-step solution

Significance of the electric potential energy

The electric potential energy depends on the sign convention of the two charges ${\mathbf{Q}}_{\mathbf{1}}$ and ${\mathbf{Q}}_{\mathbf{2}}$.

Explanation of the graph that represents the potential energy

The equation of the magnitude of the electric potential energy is expressed as,

$U\left(r_{12}\right)=k\frac{q_1\times q_2}{r_{12}}$

It can be inferred from the above equation that :

(1) $q_1$and $q_2$ must have the same sign if $\mathrm{U}>0$

(2) $q_1$ and $q_2$ must have the opposite sign if $\mathrm{U}<0$

(3) At least one of the objects is neutral if $\mathrm{U}=0$

By observation of the graph of $\mathrm{U}\mathrm{Vs}{\mathrm{r}}_{12}$,it can be concluded that the graph of $\mathrm{U}\mathrm{Vs}{\mathrm{r}}_{12}$is positive everywhere. So, the charges will be either both positive and negative.

Thus, the given graph might represent Two Protons, Two Sodium ions, Two neutrons, Two chloride ions, two electrons.