# Question #21390

Feb 28, 2017

The potential energy of the electron decreases as it comes near to a proton.

#### Explanation:

We know from physics that the potential energy $U$ of a charge $q$ at a distance $r$ from another charge $Q$ is given by the formula

$\textcolor{b l u e}{\overline{\underline{| \textcolor{w h i t e}{\frac{a}{a}} U = \frac{k q Q}{r} \textcolor{w h i t e}{\frac{a}{a}} |}}} \text{ }$

where $k$ is a proportionality constant.

The charge on an electron is -1, and the charge on a proton is +1.

Thus,

$U = \frac{k \text{(+1)(-1)}}{r} = - \frac{k}{r}$

This means that, as the electron gets closer to the nucleus, the potential energy becomes increasingly negative.