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

Question

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?

Answer 1

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.

Answer 2

No, particles have zero spatial extent in standard quantum mechanics. In fact, they are the limiting cases of waves, which do have a spatial extent. While sometimes we assign a "classical radius" to particles, these are for specific practical purposes relating to a specific physical system.

Answer 3

As written above, electrons does have not radius according to the standard model prescriptions. Just for completness, an historical result about this, older that the standard model, is given by the so-called "classical radius" of the electron. Imagine that your electron is a uniformly charged sphere with charge $e<0$. You can obtain the classical radius putting the relativistic energy at rest of the particle equal to the energy inside a charge sphere (with $e$) that has gor radius $r_{e}$: $$m_{e}c^2 = \frac{e^{2}}{4\pi \epsilon_{0}r_{e}} $$ so: $$r_{e} = \frac{e^{2}}{4\pi\epsilon_{0}m_{e}c^{2}} \approx 2.82 \times10^{-15} m$$ This result is obviously not correct, but it's just a didactical result.It makes you realize that they first thought that electrons were actual particles with definite physical dimensions

Answer 4

An electron is "felt" far away from its "position". We can apply an optical analogy: when we look at some nebulous object, we consider its geometric center its "position" despite the object is more complicated than just a point. The same is valid for an electron: apart from its position we specify some other electron properties (fields) depending on the electron actual motion. The fields are non zero far away from the electron "position". That's a layman explanation.

Answer 5

Latest experiments have proved that electrons are perfect spheres. Spheres do have volume in three dimensional space and therefore I believe although I have no evidence to show, that as perfect spheres electrons do have volume and their volume can also be calculated by the equation for a volume of a sphere in three dimensional space. In fact I believe that because of the irrationality of pi, a constant part of the equation, the volume inside the sphere is fractionally infinite what allows for an oscillation between particle-wave and responsible for spin and magnetic momentum.