Where does the energy come from

[Ben.meyer]

When electrons orbit the nuclei of an atom doesn't that take energy and where does that constant flow of energy come from?

 

[Simon Bridge]

Consider the related question: "When planets orbit a star, doesn't that take energy and where does that constant flow of energy come from?" Can you answer that one?

However - the question includes some common misunderstandings:
- Electrons do not orbit nuclei - that is an old model still used for teaching purposes.
- You do not need "a constant flow of energy" to move in a circle.
- when a free electron becomes bound to a nuclei, it loses energy, the lost energy gets stored in the electromagnetic field.