\(T_{v\,boom}=\left(\cfrac{3.4354*density}{Z}\right)^2*\cfrac{atomic\,mass*10^{-3}}{3*8.3144}\)
where \(Z\) is the atomic number, \(R=8.3144\,J\,K^{-1}mol^{-1}\).
We have,
\(T_{v\,boom}=M_m*\left(\cfrac{\rho}{Z}\right)^2*4.731*10^{-4}\)
where \(\rho\) is density, \(M_m\) is molar mass and \(Z\) is the atomic number.
The formula for \(T_{v\,boom}\) is derived from kinetic energy expression for non interacting particles which is true when the material concerned is a sparse vapor at high temperature. This means \(T_{v\,boom}\) should be beyond the boiling point of the element.
If such a \(T_{v\,boom}\) can be achieved, at this temperature, all the material disintegrate at once.
For Osmium \(Os\), the densest element,
\(T_{v\,boom}=190.23*\left(\cfrac{22590}{76}\right)^2*4.731*10^{-4}=7951.3\,K\)
which has a boiling point of \(5285\,K\).
Maybe Uranium is not necessary. Nuclear fission has nothing to do with radioactivity.
Note: In general,
\(T_{v\,boom}=\left(\cfrac{3.4354*density}{no.\,of\,particles}\right)^2*\cfrac{molar\,mass*10^{-3}}{3*8.3144}\)
where molar mass (and atomic mass) is measured in \(g\,mol^{-1}\).
\(T_{v\,boom}\) is a resonance phenomenon, at any value other than \(T_{v\,boom}\) disintegration does not occur.
Note: Maybe just upon disintegration the material particles are freed from its lattice hold and are thus non-interacting particles (other than collisions) as the derivation of \(v_{rms}\) requires. If the material is already at a vapor state at \(T_{v\,boom}\) then disintegration is instantaneous. If not in a vapor state, then disintegration occurs only on the surface where material particles can break free; which make a sealed coal containment at \(538.3^oC\) safe.
Note: Maybe just upon disintegration the material particles are freed from its lattice hold and are thus non-interacting particles (other than collisions) as the derivation of \(v_{rms}\) requires. If the material is already at a vapor state at \(T_{v\,boom}\) then disintegration is instantaneous. If not in a vapor state, then disintegration occurs only on the surface where material particles can break free; which make a sealed coal containment at \(538.3^oC\) safe.
