I've read about different models of atom proposed in 18$^{th}$ and 19$^{th}$ centuries, of which the most vital were JJ Thomson's model, followed by Rutherford's nuclear model and then Bohr's quantum model. Before posing the question I want to make it clear that I have not studied these developments and models and theories in detail because it needs a firm grip over calculus and other tools for studying the theories like Plank's electromagnetic theory Maxwell's equations, photoelectric effect and black body radiations which were fundamental for the development of Bohr's model. But I've briefly read about some of these.
Now I'm posing my question. In Rutherford's model, a major drawback was that if the electrons were in circular motion, then they would surely be accelerating and according to Maxwell's electromagnetic theory, a charged particle in acceleration would emit radiations and this would lead to decrease in kinetic energy of electrons and then the electrons would spiral into the nucleus and it's time span is about $10^{-8}s$. Then they say that this would make the atom unstable.
But my question is: Why would the electrons spiralling into nucleus make the atom unstable? I'm quite unsure about it and presently I cannot study the laws of electromagnetism and other theories as I'm not familiar with calculus and advanced mathematics. So I want not a mathematical but intuitive answer and any help is appreciated.
Best Answer
Atoms are not of dimensions one can see and touch. Mathematics is imperative to make sense of the data, otherwise one is left at the level of Democritus to whom we owe the term "atom", which means literally "cannot be cut " .
The existence of electrons was experimentally established long before the elaborate particle theories, also of ions, i.e. atoms with positive charge:
In elaborating the Democritus atom, scientists at that time had to accommodate electrons and ions and at the same time the behavior of charges. Accelerating charges radiate as you state, and orbiting charges are accelerating continuously, and thus electrons would lose energy and fall on the positive nucleus, and at best would stick and become the neutral atom, with no possibilities of "unsticking".
Orbiting charges can be envisaged to be struck off the orbit and be seen as electrons in a cathode ray tube. But if atoms were really atoms, indivisible because positive and negative charges were stuck together, there could be no electrons or ions. Thus the electrons had to have orbits and the orbits had to be stable and the road to quantum mechanics became a one way street.