Question

explain why you think electrons must be moving at a high rate of speed inside an atom. In your answer, include how the 3 particles of the atom (electrons, protons and neutrons) are attracted or repelled by each other and what forces are on an electron as it moves in its path around the nucleus of the atom

Answer 1

@mahmit2012 can you help??

Answer 2

This is a more subtle question than it may seem. You can certainly see how they *might* be moving at high speeds. Just calculate the typical acceleration (using a = F/m) of an electron located within a few pm of a nucleus, using Coulomb's Law to calculate the force exerted on the electron. It will be huge! So it's certainly *possible* that the electrons are moving quite fast, because the forces on them are enormous (relative to their tiny mass).

But why they *must* be moving fast is another story. After all, the forces on the ions in an ionic crystal are just as enormous -- but we usually imagine those ions are at rest, because the enormous forces mostly cancel out. Could that be true for the electrons in an atom as well? Could they be in some "crystal" arrangement so the enormous forces balance, and they are for the most part at rest? With nothing more than classical mechanics to go on, as in our analysis above, and of the crystal, we'd have to say yes. (This casts light on why the Thomson "plum pudding" model of the atom was a credible model for its time, knowing what scientists then knew.)

To say why the electrons *must * be moving fast, I know of only two approaches, and both are fairly sophisticated. We can appeal to quantum mechanics, and note that confined particles in quantum mechanics must have a higher and higher kinetic energy, as they are confined to smaller and smaller volumes. We could do a crude "particle in a box" estimate of what the ground-state kinetic energy of an electron confined to an atom would be, and it's very high, because the elecrton is a very light particle and it is confined withi a very small "box" (the atom).

Another approach is through classical statistical mechanics, and a thing called the virial theorem, which says there is a statistical relationship between the kinetic and potential energy of systems at equilibrium, and the kinetic energy generally is twice the magnitude of the average potential energy. We know the potential energy of the electron in the atom is substantial (Coulomb's Law again), so we may conclude the kinetic energy must also be substantial, and estimate its magnitude.

These two approaches tell us the kinetic energy of an electron in an atom must be high, and therefore they must be moving fast. It does NOT forbid the case of electrons being essentially confined to individual positions, like the ions in a crystal lattice, and vibrating furiously in place rather than orbiting in the way satellites swing around a planet. And in fact, we know very little about the actual motion of electrons in an atom. We tend to think informally they are orbiting like satellites, but it isn't obvious to me that an "electron crystal" picture might be equally sound.

Neither of these approaches is elementary. I can't really think of any elementary *proof* that the electrons must have high kinetic energy, though. But you do have an easy argument, above, on why they *can* be.

Answer 3

thx