# Physicists talk about the electron in a hydrogen atom being in an “energy well”. Explain why the difference in energy, ∆E, is negative. What does a negative ∆E represent?

##### 1 Answer

#### Answer:

#### Explanation:

Taking a nucleus as a point charge of electrostatic charge

Note that

The electrostatic potential energy of the electron is defined as the energy it takes to bring them apart to an infinite separation, such that there no longer any interaction between the two particles. [2] The relationship between this energy, the charges of the two particles, and their initial separation

*takes* energy to split them apart.

Plotting (in two dimensions) the electrostatic potential energy against the separation between the two charges shall give something that looks like half of the cross-section of a well- the smaller the separation, the lower the electrostatic potential energy. And that's why the electrostatic interaction behaves in a way similar to gravity acting on an object in a well.

graph{-1/x [-1.315, 8.685, -4.8, 0.2]}

FYI: With some knowledge of calculus it is possible to derive this expression by integrating the magnitude of their separation with reference to the separation, from the initial distance to the final separation of infinity