Sizing Particles Up

Knowing that the particles are passing at velocity $v$ in the Faraday Dark Space of a discharge tube,

it would be possible to flash X_ray through an aperture at an appropriate frequency, $f$ to obtain a still scattering pattern of each type of particles, $a_{\psi\,c}$,  $a_{\psi\,ne}$ and $a_{\psi\,\pi}$.

Given some reference, their size ($a_{\psi\,c}$,  $a_{\psi\,ne}$ and $a_{\psi\,\pi}$) can be determined.

At this point,  although the argument for the existence of $a_{\psi\,c}$ is plausible, particles need not have quantized sizes.  Particle size need not be in integer multiples of $a_{\psi\,c}$.  The requirement,

$a_{\psi}=n*a_{\psi\,c}$

$n=1,\,2,\,3...$

need not be true.