# Confused about the sizes of atomic particles

1. May 16, 2013

### warfreak131

Hey guys, I was doing some research and I am confused since I can't seem to get a straight answer.

I wanted to know what the diameters/radii of protons and electrons are. But no place I go to agrees on the numbers. The general trend for protons is somewhere around 10^-15, but I've seen estimates go to 10^-13 to 10^-18. I've also seen estimates where the electron radius is bigger than the proton radius, so it's very confusing.

Are there any well accepted values for these?

2. May 16, 2013

### ModusPwnd

The problem is that elementary particles are points (so far as we know). They have no size. The proton is not elementary, so you can roughly define a radius by its internal structure. So why does an electron, a point particle, have a size at all? Usually, if I recall correctly, its radius or size is defined as some portion of its wave function. A few std. deviations or nintey some percent of its wave function. (are you familiar with a wave function from quantum?)

Also, consider atomic orbitals you see in chemistry. They are filled with an electron or two, and they are not only different sizes but they have different shapes! Because the electrons in an atom are bound to the atom their wave function changes and thus their "shape" is different. But this shape is simply where the bulk of their wave function lies, they are "really" point particles.

3. May 16, 2013

### warfreak131

I have taken modern and quantum physics, and I am familiar with wave functions, but the functions we worked with only dealt with the probability of it being at a certain point R away from the nucleus, or it's expectation value, not the radius of the electron itself.

4. May 16, 2013

### Staff: Mentor

As far as we know, electrons and other truly fundamental particles are "pointlike", that is, they have no measurable size as a fundamental property. Think of it as the size of the object "inside" its quantum-mechanical probability distribution. The size of that distribution of course depends on the particle was produced and the environment in which it propagates.

When we try to measure the "true size" of the electron, all we get (so far) is an upper limit on the size. That is, the electron might really have some size that is smaller than that, but it would not affect any of our experimental results (so far).

From the Wikipedia article on the electron:

http://en.wikipedia.org/wiki/Electron

5. May 16, 2013

### DEvens

Sure. Because, so far as we are able to tell, an electron does not have any internal structure. As ModusPwnd said, it's elementary. That is, it does not have any internal "working parts." We don't actually have a measured size, just upper limits. Those limits are getting pretty small.

A proton is "made up" of three quarks and some gluons. These spend their time some distance apart on average. So a proton behaves like a blob of stuff with a (very small) finite size. It scatters other particles very differently from how it would if it were zero size. It shows three scattering centres. The quarks are, so far as we can tell, elementary. They have not, as yet, shown any internal structure.

The definition of the size of a proton is kind of complicated. You can look at things like the distance the quarks appear to be under scattering by different energy or type of particles. Such as when you scatter them off other protons. Or off anti-protons. Or off electrons or positrons. Or when you scatter alpha particles off of them. You can also use the size as estimated based on various calculations from various phenomenological (or semi-phenomenological) models. (It's pretty cool that the spell checker here had no problem with that term.) For example, there has been a lot of work done on things like the bag model of protons. You can also get an estimate from things like nuclear interactions and stacking in things like larger atomic nuclei. You can estimate the size of a uranium nucleus (say U-238) from scattering, and then say that a proton is 1/238th of that size. There are semi-phenomenological models for nuclei such as the liquid drop model. And there are some results from numerical schemes like lattice gauge calculations.

Another method is by studying the energy levels of atoms. Because the proton, and the neutron, have finite size, the electric charge distribution of the nucleus is not point-like. That produces a minor perturbation on the energy levels of electrons in an atom. By measuring these perturbations we can get some idea of the size of a nucleus. That was a keen 4th year homework assignment that wound up requiring a lot of pages of algebra.

And each of these methods gives a bit different answer.
Dan

6. May 16, 2013

### warfreak131

Awesome, thanks for the replies gents, I understand it much better now.

7. May 16, 2013

### Popper

You might do some searching using the term "deep inelastic scattering". You might find your answers using that term. That's what they used to probe the gizzards of a proton.