Question

What was a major flaw of Rutherford's planetary model of the atom?

Answer 1

There were probably several flaws, but one big one was the fact that the electrons somehow stayed in stable orbits that would not be allowed by electromagnetics.

Explanation:

According to the classical theory of electromagnetism, a charged particle that accelerates through space gives off electromagnetic radiation (https://www.google.com/url?sa=t&source=web&rct=j&url=https://www.cv.nrao.edu/course/astr534/PDFnewfiles/LarmorRad.pdf&ved=0ahUKEwi0x5eJ9IzXAhWmslQKHYiEA0QQFggpMAE&usg=AOvVaw2SapwhcJKzU9aUeMvid_Xj). That includes an electron orbiting a nucleus, which is accelerated perpendicular to its motion as it goes round. But the energy of that radiation can't come from nothing. It has to come from the electron falling into the nucleus so the atom cannot last.

That does not really happen, of course, because we know now from quantum mechanics that the electron is not a little ball of concentrated charge orbiting around the nucleus. The Heisenberg Uncertainty Principle (https://en.m.wikipedia.org/wiki/Uncertainty_principle) combined with the very small mass of the electron means the electron is fuzzed out into a cloud that envelops the nucleus, not orbiting it. In effect the electron has already "fallen in" but its cloud of probability distribution is too bulky to be completely absorbed.