Question

If the potential energy between electron and proton at a distance r is given by $U=-\left(\frac{k{e}^2}{3r^3}\right)$. The force is :

• A. $F=\frac{k{e}^2}{r^2}$
• B. $F=-\frac{3}{4}\frac{k{e}^2}{r^4}$
• C. $F=\frac{k{e}^2}{r^4}$
• D. $F=\frac{k{e}^2}{r}$

Answer 1

The correct option is C $F=\frac{k{e}^2}{r^4}$

$F=-\frac{du}{dr}$
$=-\frac{d}{dr}(-\frac{K{e}^2}{3r^3})=-\frac{K{e}^2}{r^4}$