# The stability of an atom

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.

• An electron spiralling into the nucleus poses a difficulty because if it were so the atom-electron system would lose its energy and collapse. It would form a Thompson's model of sorts. Which isn't the reality. For emitting radiation you need an energy source. And the source of the energy would be the motion of the electron. The radius of the electron of the orbiting electron would increase while the energy of the emitted radiation would subsequently increase. – Kunal Pawar Apr 9 '17 at 17:18
• > this would lead to decrease in kinetic energy of electrons - no, it would lead to decreasing of total energy of the system, which would manifest in decreasing the radius of the electron's orbit and increasing its kinetic energy. The increase of kinetic energy would be because in central attractive field of force, orbital velocity increases with decreasing orbit radius. – Ján Lalinský Apr 9 '17 at 19:52
• How can an atom that exists for only $10^{-8}s$ be described as anything other than "unstable"? – sammy gerbil Oct 4 '18 at 14:11
• @sammygerbil The atoms exists even after $10^-8 s$. It's just that the electrons will get stuck to the nucleus, and I don't think that would make the atom "unstable". – Abhinav Dhawan Oct 5 '18 at 10:07
• @AbhinavDhawan The atom is the arrangement of the electrons in orbit around a nucleus. If the electrons are stuck in the nucleus, the atoms cannot make the transitions which Bohr's model predicts, they cannot emit the distinct wavelengths of light which are observed, they cannot take part in chemical reactions. Their atomic properties cease to exist, they cease to be atoms. Moreover, in the process of electron capture the electrons will combine with protons to form neutrons. – sammy gerbil Oct 5 '18 at 10:20

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:

ion, This term was introduced by English physicist and chemist Michael Faraday in 1834 for the then-unknown species that goes from one electrode to the other through an aqueous medium

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.

• Thanks for your answer. One last concern is that everywhere it is asserted that atom would lose its stability if electrons spiral into nucleus. But isn't the term 'unstable' misleading because the sticking of electrons to nucleus would make the atom chemically inactive ( it can no longer lose or gain electrons) and not unstable. Rather it would be chemically more stable. Anyways the chemical inactivity of atom leads to a major drawback of Rutherford's model and with your help I could grasp this but still regarding atom as unstable puzzles me up. Hope you can help. – Abhinav Dhawan Apr 10 '17 at 2:54
• It comes from the Bohr model. One can find classical electromagnetic solutions with the electron orbiting the proton, but they are unstable as the smallest perturbation ( a radiation is a perturbation) destroys them and starts the spiral. So Bohr imposed by postulates the stability.That is where the term stability comes from. – anna v Apr 10 '17 at 3:24

It would make the atoms unstable in the sense that they would quickly collapse to essentially a single point as the electron spiraled closer and closer to the nucleus. In other words, atoms of the size that we observe could not stably exist.