How can scientists measure the radius of an atom?

Answer 1

The radius of an elementary particle is deduced from its cross section.

The cross section is determined in some kind of scattering experiment where one elementary particle is made to collide with another. This collision process is the main task at the various particle accelerators around the world.

There are very technical definitions of cross section because the cross section of an elementary particle is calculated within the theory of quantum mechanics. Even so, the basic idea stems from our understanding of the "size" of a particle in classical terms.

This answer will give a qualitative idea. We describe all these particles as though they were round which is almost always true.

A cross section is an area. For a macroscopic classical (spherical) particle, if one shines a light on it, it will cast a shadow. The shadow will be round and the same size as the particle. That shadow is the cross section. (When defining cross section we assume the light rays are coming from a great distance so they may be taken as parallel and the shadow is cast on a flat surface directly behind the particle and perpendicular to the incoming light beam.)

With a shadow, one could take a ruler and measure its size, but in scattering experiments one usually has some kind of incoming beam hitting millions of particles and they all contribute to the "shadow" so you can't just use a ruler.

In the classical definition given above, the light rays are either blocked or get past the object. (Diffraction can occur, but that is actually OK and is considered part of the cross section measurement. One need not consider it at this stage to get the basic idea.) One can use that fact and measure how much light was blocked and work backwards to figure out how large the particles were which were blocking the light. If the amount of light that was blocked reduced the light by an amount equivalent to an area, A, then A divided by the number of particles gives you the area that each one blocked. Cross section is area per particle and area is pi times radius squared, so you calculate the radius of the particle. (Scattering is always defined for a case when the number of scattering particles is so small and they are so dilute that there is no significant chance that the shadow of one particle covers another particle.)

The above classical description is used in the more sophisticated case when a beam exotic particles of one sort are made to collide with a target of other particles. One just figures out how many of the incoming particles were deflected from the path of the incident beam and you work backwards to calculate cross section and use pi r squared to get the radius.

The only problem with this generalized approach is that the incoming particles have their own radius and are not so small compared to the target particles. With the light, it was treated as though it had infinitesimal particles and that is adequate when light meets a macroscopic particle.

In the classical case, a beam of particles of radius r1 striking a target with particles of size r2 would would remove from the incident beam a fraction of particles determined by the combined radius, i.e. pi times (r1+r2) squared. In the actual case of quantum scattering, essentially the same thing happens but the "size" of particles does not depend on just the apparent radius of each particle. Experimentally, the different results do not arrange themselves so simply and it is as though the sizes r1 and r2 change every time you change the particles. Worse than that, the cross section changes with the speed of the incident particle.

The ultimate resolution is that experimentally you just say what the apparent combined cross section is for both particles. Further, you say what it is at each different energy measured. In fact, it turns out there are other factors as well, but they get even deeper into the quantum nature of the particles.

Answer 2

The distance between nuclei of two atoms is taken and divided by 2

Answer 3

picometers