Why don't electrons fall into the nucleus?

No.

Air resistance is the net force of air particles (ie oxygen, nitrogen, carbon dioxide, molecules, etc) hitting the object - causing it to slow down.

As Rutherford proved, atoms are almost entirely empty space (excluding the nucleus and the electrons). Therefore, there are no particles on a subatomic scale which exert this force. The space within an atom is essentially a vacuum and is exhausted of particles. So there is no resultant force on the electron.

The starting force is simply the electrostatic attraction between the positively charged nucleus and the negatively charged electrons.

If there is no electrostatic force acting on the electron (ie no nearby protons) I would assume the electron continues in a straight line at a constant speed until acted on by a force.

Why they don't fall into the nucleus is a lot more complicated. According to Heisenberg, electrons cannot have a defined location within the nucleus - so it occupies the rest of the space in many different ways. If the electron was specifically certain to be within the nucleus, its momentum becomes exponentially uncertain. Instead they occupy energy levels outside of the nucleus.

Electrons do not orbit the electrons. Not in the conventional sense. This is one of the many lies you have been taught at GCSE and A level. Look up the electron cloud and quantum mechanics.

The best explanation to the best of my feeble understanding to your questions are: In an atom there isn't any air to resist the electron, air resistance is caused by air, which is nitrogen oxygen etc. Most of the atom is just empty space. There isn't a starting force to start the electron up, like a motor or something. The electrons are not orbiting, as said above. Particles behave very strangely at subatomic level, which is where quantum mechanics come in. Forget about the classic Newtonian physics, F =/= ma at this level. You cannot directly observe the electrons, as stated by quantum mechanics, and therefore we estimate where each electron is most likely to be at each point in time and "work out" a path for the electrons. The common(only?) ones are the s, p, d, f. It is very similar to calculus where we take the limit of something without working anything out that is specific. I hope this make sense. Quantum mechanics is similar to calculus, at least in my understanding.

Because they're electrostatically attracted to the nucleus. Of course though, this is a massive oversimplification and electrons are not really these little particles orbiting a nucleus, it's just easier to imagine them like that.

Yep, but since the electron is changing direction during it's orbit, the acceleration of the electron is also changing, so shouldn't the direction of the force also be changing so it must have a resultant force to continue acceleration, and so this is caused by the continuous electrostatic attraction.

I know about this and that electrons are in fixed quantum energy states, but doesn't the acceleration of the electron cause it to emit EM waves which should mean it loses energy and decelerates overall?

Also, the probability density for an electron is not non zero within the area of the nucleus, so there is a (very small) probability that it could fall into the nucleus? What would happen in this event? For example, in the n=1 state hydrogen, the most probable position for the electron is at the nucleus itself, so why don't we find it there?

My question is more to do with WHY the electrons are set in specific quantized energy states and quantized energy levels rather than just accepting that they are.

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So what force causes the electron to orbit in the first place then? There must be a 'starting' force to get the electron around the nucleus in the first place and from there, since there is no resistive forces acting on this scale it would continue to accelerate at a constant velocity? What would happen if you removed the proton (say we have a hydrogen nucleus), would the electron just stay at rest?

Also, why doesn't the electron simply fall into the nucleus due to the net positive charge in the nucleus and the negative charge on the electron causing electrostatic attraction between the two?

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The orbiting electron analogy evolved into the more accurate Bohr-Rutherford model, but even this model falls apart exactly because it does not predict the behaviour of the atom for the reasons you have identified.

In other words it's simply wrong and no planetary-orbital model can predict the behaviour of the electron.

To get a better model one has to embrace quantum mechanics (which was developed to answer this paradox) and at a simple level of abstraction, you have to completely disregard the idea that electrons have a defined trajectory.

It's also more appropriate to think of the electron not as a particle but as a wave and a representation of energy.

In quantum mechanics, electrons are defined as having discreet energy levels constraining the space they are allowed to occupy around the nucleus. It also predicts that electrons cannot occupy the same space as the proton. Quantum theory is wierd in the extreme and the classical definition of causality for every event does not apply.

In essence, when you get down to physics at the sub-atomic level the 'why' question cannot be answered because it's the limit of physics knowledge.

The mathematics describes the observations of the atoms behaviour to a high degree of precision. But it does not explain why they happen.

Richard Feynman quotation:

"What keeps the electrons from simply falling in? The uncertainty principle: If they were in the nucleus, we would know their position precisely, which would require them to have a very large, but uncertain, momentum, i.e., a very large kinetic energy. This would cause them to break away from the nucleus. They make a compromise: they leave themselves a little room for this uncertainty and then jiggle with a certain amount of minimum motion in accordance with this rule."

Still a lot more Nobel prizes to be had if you can get closer to the answer!

Shouldn't air resistance when orbiting should cause them to decelerate and eventually stop orbiting or even fall into the nucleus due to the opposite charges between the two?

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Why are we turning simple chemistry into very complicated physics??? My head hurts....

It's not that simple. Simple chemistry tells you that opposite charges attract, but it also tells you that the electron has a negative charge and the nucleus has a net positive charge. Simple chemistry doesn't explain why the small electron doesn't just fall into the much larger nucleus.

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All chemistry is kind of simple....

All chemistry is kind of simple....

Not sure if trolling

No it's not, a lot of the electron and sub levels go into QM. The electron excitation is explained by this. Even hybrid orbitals are explained.

There's a lot more to learn yet. It's all at degree level.

I don't mind having to learn all that because I love chemistry so no matter how hard it gets I'll still love it

All chemistry is kind of simple....