# Q & A: Why don't electrons fall into the nucleus?

Q:
Why doesn't the electron get sucked into the nucleus since the nucleus is positive and the electron is negative?
- matt (age 16)
mentor, oh, usa
A:
Matt -

That's a really great question!

The picture we often have of electrons as small objects circling a nucleus in well defined "orbits" is actually quite wrong. The positions of these electrons at any given time are not well-defined, but we CAN figure out the volume of space where we are likely to find a given electron if we do an experiment to look. For example, the electron in a hydrogen atom likes to occupy a spherical volume surrounding the proton. If you think of the proton as a grain of salt, then the electron is about equally likely to be found anywhere inside a ten foot radius sphere surrounding this grain, kind of like a cloud.

The weird thing about that cloud is that its spread in space is related to the spread of possible momenta (or velocities) of the electron. So here's the key point, which we won't pretend to explain here. The more squashed in the cloud gets, the more spread out the range of momenta has to get. That's called Heisenberg's uncertainty principle. Big momenta mean big kinetic energies. So the cloud can lower its potential energy by squishing in closer to the nucleus, but when it squishes in too far its kinetic energy goes up more than its potential energy goes down. So it settles at a happy medium, and that gives the cloud and thus the atom its size.

(published on 10/22/2007)

## Follow-Up #1: Does the electron have a position?

Q:
But if we are saying that there is a probability of finding something here or there, this means that it must be somewhere at a definite place, it is just that we do not have the means to know without errors where is it. So if the position is definied but cant be determined, then how actually is the motion of the electron. I dont want to determine where it is, what is its momentum etc.
- Amol Bhave (age 16)
A:
Your interpretation is what common sense would initially lead us to believe. However, we know that it isn't true. The electron is truly spread out. If these quantum variables (such as the electron position) that seem to be spread out had actual hidden values, then a set of experimental predictions known as the Bell Inequalities would be obeyed. In actual experiments the Bell Inequalities are consistently violated. Therefore the spread-out variables really are spread out.

The process of interacting with a large apparatus that's sensitive to where the electron is causes the formation of a state in which the electron's cloud has much less spread. This occurs via a quantum process called decoherence. There's no consensus about whether a single such state arises or a collection of states covering the whole range of possibilities.

Mike W.

(published on 12/04/2011)

## Follow-Up #2: electron cloud in atom

Q:
So according to you, the electrons will be present mostly in the volume where the kinetic & potential energy are almost same.Does the electron move in a circular path in this region?if so why doesn't it radiate energy?
- ashwin gopal (age 16)
ernakulam,KERALA,INDIA
A:

The electron is present as a cloud. Averaged over the cloud, the positive kinetic energy is half as big as the negative potential energy.

More importantly, the cloud really is the state of the electron. It's not a picture of where some dot-like particle probably is. It isn't anywhere in particular. It also doesn't have any particular velocity.  In a hydrogen atom, it's certainly not going in a circle. The cloud doesn't go anywhere at all. There's no reason for it to radiate.

The world at a small scale cannot be put together out of anything like the pictures we're used to at a large scale.

Mike W.

(published on 08/01/2013)

## Follow-Up #3: what are electrons doing?

Q:
I want to ask about the electron. I love quantum mechanic and astrophysics. I've heard about this electron cloud and I google it for a while. I think I get the message, that is - At any given moment electron can be found at random place in the electron cloud (described with the wave function). What I don't understand is how you can see the electron and determine his position? And if you take snapshot how can you be sure that the electron doesn't move around this cloud? I mean, the electron must be moving in some pattern way but I think that he is so fast that we think that he is at many places at the same time or he simply disappear on one place and show up at another. Can this be true? Can you tell me the cutting edge, there must be something more than just saying that the electron can be everywhere and nowhere. Thank you!
- Alexander (age 21)
Skopje
A:

Alexander- Your question has a lot in common with many others, so I've put it in a thread.

There are a variety of ways that an electron, which is always a spread-out wave,  can be found to be in a smaller-than-usual region. Maybe it bumps into a piece of film, which localizes the wave to the region of one little bit of silver.  Maybe the electron just got emitted from the fine tip of a needle, so you know it's very close to that tip. Maybe a high-energy gamma ray bounces off of it, so that the position of the electron can be nearly determined from the gamma ray position and direction.

As we discuss at numerous points (search for "Bell Inequality") the ranges of positions and of velocities are not due to our ignorance of some fast rattling around, but are a description of what the electron wave actually is.  It's not that it is "in" the cloud, it is the cloud. Once the electron cloud has a small size than you can be sure that the electron is rapidly moving, in a broad range of directions, so that cloud will start to spread out.  If the cloud is already highly spread out, the electron may not be moving much. This relation is called the Heisenberg Uncertainty Principle.  Things people wrote about it before the Bell Inequality violations were established are generally outdated. They are still usually repeated in popular presentations and in some textbooks.

Mike W.

(published on 09/10/2013)

## Follow-Up #4: particle clouds

Q:
So from reading your thread where you answer several questions relating to the position of the electron in which you say that the electron has no defined measureable location but intstead exists as a wave probability function a set of positions in space where you might find the electron each position with a certain probability and that the electron doesn't exist, even from an absolute perspective, at any one of these points at any given moment but as all of these points at once in a sort of cloud. This much I understand but what I don't understand is why, why is it that an electron has this cloud like existance instead of a definite location I heard you mention the Heisenberg uncertainty principal that the more you know about a particles velocity the less you know about its position or visa versa but why is this that an electron exists as a cloud whereas on a macroscopic scale I have certainty of position and velocity, why is an electron a quantum wave probability function cloud thingy?
- Eric Fernandez (age 16)
Helena, MT, United States
A:

We don't really know why the world is made up of quantum waves rather than of little dot-like things, or some other possibility. That's just how it is. The Heisenberg uncertainty principle isn't really the reason for the quantum form of things, just one of the many mathematical consequences.

The thing that has to be explained, in a world made of quantum objects, is not why little things are fuzzy. That's just part of the basic description. What we have to explain is why we experience a world where big things have fairly definite positions. They do still have, so far as we can tell, a little quantum fuzz, but it just isn't very noticeable on a big scale. What we have trouble talking about is why we see no Schrödinger cats that are both alive and dead. That's the issue addressed, more or less, by various interpretations of quantum mechanics.

Mike W.

(published on 10/30/2013)

## Follow-Up #5: uniting quantum mechanics and relativity?

Q:
Mike says, in this answer, that the problem is not why things on the quantum scale are fuzzy, but why things on the big scale are definite. He says why don't we see Schrodinger's cats that are both dead and alive. Well, Einstein said everything that ever happened or will happen is all present simultaneously, it's just that we can't experience it all as we are limited by our location and direction of motion. So maybe those cats are out there both dead and alive, at different times, but all their times are really simultaneous. Would this be any kind of union of quantum physics and relativity?
- Charles (age 73)
Carmel, NY, USA
A:

Your idea is very close to what's called the Many Worlds interpretation of quantum mechanics. The main difference is that the mathematical axis separating the "worlds" is not an extension of the familiar time variable, but rather an extension of variables from quantum descriptions. David Mermin has discussed an analogy between the way a particular experience arises from the broader quantum state and  the way a particular sensed "now" arises from a 4-D relativistic world. That also seems very much along the lines you're thinking.

One union between QM and relativity is quantum field theory, quantum mechanics in a form consistent with Special Relativity. That's the form of quantum mechanics used in ordinary fundamental work.  There are attempts, e.g. String Theory, to unite QM with General Relativity. Those attempts are not yet fully successful. It's conceivable that there's a connection between that dangling end and the dangling end of quantum interpretation. No one yet knows.

Mike W.

(published on 10/26/2014)

## Follow-Up #6: when does quantum measurement occur?

Q:
So, the electron is a cloud around the proton and has no definite location or more correctly we can't know it's position and momentum at the same time. That's not hard to understand, there are no means in existence (as far as we know) to measure the both. Hence the uncertainty principle. What happens when we strip the proton of the electron and shoot it towards a target? We know it propagates through space as a wave. But when it arrives at and hits the target - what state is the electron in at that moment? Is it a cloud of probabilities, is it a wave or is it a tiny, material, point like particle with clearly measurable physical properties like mass, speed, momentum and position? My understanding is that it is the latest, because we end up with a tiny witness mark on the target (the screen). But only if we care to observe. Let say we don't do that and walk away. A million years later when someone looks at the screen, he'll see the witness mark. Now the question is WHEN did the witness mark appear - when the electron initially hit the target, but we didn't care to look at it, or a million years later at the moment when the first observer happened to look at the screen? What was the state of the point where the electron hit the screen during those one million years?
- Emil Raytchev (age 56)
Illinois, USA
A:

People still have many ideas about quantum "measureent", so the questions you ask don't have consensus answers. In most modern interpretations, however, we can answer some of these.

The electron really doesn't have an exact position and momentum. It's not just a matter of what we know about it.

The small-region "witness mark" forms as the electron hits the target, e.g. a photographic film. Typically, the cloud that arrives would be consistent with marks forming at a range of positions. Yet we only see one.  How can that be? The biggest unsettled question is whether the set of quantum outcomes collapses to just one mark or extends to include multiple versions of you, each linked to just one mark. The former (collapse) interpretation seems more in line with our intuition, the latter one (many worlds) seems closer to the math of the quantum processes. There are problems with either approach, and with attempts to evade the whole question.

Mike W.

(published on 08/03/2018)