# Do electrons have a radius when they behave like a particle?

I know sometimes electrons behave like waves, but it sometimes can be seen as a particle. while it's a particle, does it have a radius? or, a volume? If it doesn't even have a volume, how can we still call it a particle?

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If you like this question you may also enjoy reading this and this posts, and links therein. – Qmechanic Jul 5 '13 at 8:17

An elementary particle is not like a billiard ball at a very small scale. You yourself state

i know sometimes it behaviors like a wave, but it sometimes can be seen as a particle.

This statement does not apply to macroscopic particles, it applies to microscopic quantum mechanical entities when the dimensions become equal or smaller than a billionth of a meter, a nanometer. We sometimes call these entities particle and sometimes call them wave.

We call them wave when interference phenomena appear, characteristic of wave equations , and particles when they appear like the center of mass coordinate of a macroscopic particle, i.e. have an $(x,y,z,ct)$ in space and a $(p_x,p_y,p_z,E/c)$ in four momentum space.

while it's a particle, does it have a radius?

No, the elementary particles in the standard model do not have a radius, they are assumed point like.

or, a volume?

Neither a volume.

if it doesn't even have a volume, why do you say it's a particle?

Because it behaves kinetically like the center of mass of a macroscopic particle, which describes the kinematics of it. It is a linguistic compromise that describes an elementary entity's kinematic behavior under certain conditions. These are the results of theoretical fits to very many experimental observation during the last century.

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i know sometimes it behaviors like a wave, but it sometimes can be seen as a particle.

Firstly, the electron has a wavefunction $\Psi$, which is a wave, but when it looks like a single point (particle) when it is observed because this wave is actually just the probability amplitude of finding the electron at a certain point, with the probability density being $|\Psi|^2$. You seem to be thinking that the electron thinks "Ok, let me be a wave now". "Let me now be a particle!" or something like that, but it is not like that. It is a particle, its wavefunction is a wave.

while it's a particle, does it have a radius? or, a volume?

In standard Quantum Field Theory, and Quantum Mechanics, electrons are generally thought of as point particles, which means that they have no spatial extent.

However, in string theory, they are supposed to have some spatial extent, such as fundamental strings (with length), D2/M2 branes (with areas), D5/M5 branes (with 5-volumes) and so on. But I don't think that that is what you vwere aking..

if it doesn't even have a volume, why do you say it's a particle?

There is no standard definition of a particle. A particle is generally just something with a very small volume as compared to the other things in the system you are considering. For example, if you are kicking some sand into the air, the grains of sand can be considered as particles. If you are considering the sun and the Milky Way, the sun can be considered as a particle, the Milky Way can be considered as a particle in the observable universe, and so on.

I think what you mean here is an elementary particle, i.e. which cannot be broken down. In standard QFT, and QM, these elementary particles are point-particles, with absolutely no spatial extent, so that no matter what you are comparing it to, considering it as a particle is always exact (because the ratio of the elementary particle's volume to the other object's volume is always 0, or 0:1, if you like. Having 0 volume actually makes things exactly a particle, not "not a particle" as you seem to have a the misconception. ......

But in string theory, of course, as I have said before, they have some spatial extent.

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