A proton is positively charged. An electron orbiting the proton is negatively charged (eg. the hydro

Asked by omair1993 | 29th Jan, 2009, 07:34: PM

Expert Answer:

As we’re dealing with quantum theory, there is, unfortunately, no simple classical “billiard-ball”-style answer as to why electrons don’t spiral into the nuclei of atoms. Having said this, we can think of this phenomenon (i. e. not spiralling) as being caused by some sort of a “quantum repulsion” due to Heisenberg’s uncertainty principle that forces electrons to keep their distance (at least on average) from the nucleus.

To begin this explanation, let us think about how the energy of an electron varies as it spirals inwards towards the nucleus. Classically, its total energy decreases due to the fact that it radiates energy in the process.

Things, however, are somewhat different in quantum theory. It says that if an electron is so close to the nucleus that it’s always within a distance of it, then Heisenberg’s uncertainty principle dictates that we can’t know (the magnitude of) its momentum p any more accurately than about , where , where is Planck’s constant.

This means that, hypothetically, if an electron started to spiral into its nucleus that, as it did so, we would tend to come to know less and less about its momentum due to the fact that would tend to decrease. This, in turn, would mean that it would probably become more likely that the magnitude of was very large. It would also imply that the electron’s energy would tend to become large as , , where is mass and is potential energy.

Thus, if an electron did start spiralling into its nucleus, Heisenberg’s uncertainty principle would tend to cause its energy to actually increase (at least on average) as it got closer and closer due to an increase in the uncertainty of its momentum.

Such a pattern of movement would thus be unstable as the electron could probably lower its energy by moving further away. In other words, it’s as if there’s some sort of a quantum repulsion caused by Heisenberg’s uncertainty principle preventing the electron from spiralling in too far. Arguably, this is a large part of the reason why electrons don’t spiral into nuclei due to Coulomb attraction.

We should note here that, even forgetting about quantum physics, electromagnetic attraction alone would not cause an electron to spiral into a nucleus. This is because a central force by itself does not cause an orbiting object to spiral in. It may, for instance, cause it to move in uniform circular motion instead.

The main reason why classical physics predicts that electrons spiral into nuclei is that it says that their orbital acceleration causes them to radiate energy, thus decreasing distance at which they orbit the nucleus.

We should also mention that another reason why electrons don’t spiral into their nuclei is because quantum theory constrains how they can emit radiation. More specifically, it only allows these particles to radiate in a way consistent with them jumping from one energy level to another. In other words, quantum theory’s discrete nature forbids electrons from gradually spiralling inwards. This limitation is another facet of the explanation of why electrons do not spiral into nuclei.

One final point that we should be aware of is that electrons are, obviously, not like tiny little billiard balls circling around nuclei like planets orbiting the sun. Instead, it’s natural to think of them as being smeared out ‘clouds’ that extend over some region surrounding the nucleus. (Having said this, it can sometimes be helpful to think of electrons as orbiting their nuclei.)

 

Answered by  | 30th Jan, 2009, 12:37: AM

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