Is this valid for a solid?; atoms in a regular lattice being bombarded with temperature particles or electric charges,
\(E_{input/atom}=\cfrac{1}{2}c^2*{density}*{Z}*3.4354\)
\(v_{boom}={density}*{Z}*3.4354\)
where a unit volume moves across with velocity \(v_{boom}\) to provide the necessary energy input per atom.
Compared with per particle view,
\(E_{input/particle}=\cfrac{1}{2}c^2*\cfrac{density}{Z}*3.4354\)
\(E_{input/particle}*Z^2=E_{input/atom}\)
This will be a high number; the associated \(T_{boom}\) is even higher by a factor of \(Z^4\).
For iron, \(Z=26\), density \(7874\,kgm^{-3}\) and molar mass \(0.055845\,kgmol^{-1}\)
\(v_{boom}=3.4354*7874*26=7.0331e5\,ms^{-1}\)
\(T_{boom}=7.0331e5^2*\cfrac{0.055845}{2*8.3144}=1.6611e9\,K\)
This is hotter than the Sun. Only photons at light speed can provide such energy on the small particle scale. An atom is indestructible, as a atom!
Good night.
