I found this question in Quora.com, and it was asked by an eighth grader. I don’t know how that student came up with this question, but it used to be a big question which led to a Nobel Prize solution afterward.

There are two steps to think of this problem. First, people would think that the electron can rotate about nucleus such that the earth rotates about the sun.

In mechanics, the centripetal force on the earth gets balanced with gravity from the sun. That’s why the earth doesn’t fall into the sun. (The reality is more complicated, but basically the motion is stable.)

But if you calculate how the electron rotates with electric force from the nucleus as above, the electron MUST fall into the nucleus! (People used electromagnetism, too, for this problem.)

So that’s the real problem at that time. So, a physicist assumed that the energy taken by the electron is fixed. Then, he proved that the electron doesn’t have to fall into nucleus.

That assumption was one of the first start points for the quantum theory. But, as you know, quantum theory can even explain this assumption.