Understanding Atom Orbits: Calculating Lost Energy

[Bjarne]

Once it was thought that electrons was orbiting nucleus almost like planet the Sun.
But this could not be correct because then would the electron lose their energy and spiral into the core.
My question is how such orbit energy lost can be calculated.

This is not homework.

 

[phyzguy]

Classically, an accelerated charge emits radiation. The Larmor formula tells you the total power emitted by an accelerated charge, and it $$P=\frac{2e^2a^2}{3c^3}$$, where e is the electron charge, a is the acceleration, and c is the speed of light. If you assume the electron is orbiting the nucleus, you can calculate the centripetal acceleration and how long the electron takes to spiral into the nucleus. It doesn't take long!