Hydrogen, \(H_2\), with \(Z_m=2\), density \(0.08988\,gL^{-1}\), molar mass \(1.00784\,gmol^{-1}\)
\(v_{boom}=3.4354*\cfrac{0.08988}{1*2}=0.154\,ms^{-1}\)
\(T_{boom}=0.154^2*\cfrac{1.00784*10^{-3}}{2*8.3144}=1.44e-6\,K\)
This is way low, practically at zero Kelvin.
Water at \(80^oC\), with a density of \(971.8\,kgm^{-3}\),
\(v_{boom\,water}=3.4354*\cfrac{971.8}{10}=333.85\,ms^{-1}\)
Which is about lightning speed of \(332\,ms^{-1}\). Is lightning nuclear? What raise water temperature to \(80\,^oC\) in the first place? Density of condensed water droplets in the air could change with air currents to \(971.8\,kgm^{-3}\) without an increase in temperature. It is just mixing air into water to bring down the density of water.
\(v_{boom}\) causes the lightning to race at \(v_{boom}\) speed after initiation because the particles exit/separate at \(v_{boom}\) speed (post "Sonic Boom" dated 14 Oct 2017 and post "No Solution But Exit Velocity Anyway" dated 14 Jul 2015). But, how does lightning start?
Given temperature, the spread of velocities (Boltzmann distribution) among the water molecules provides that some are at \(v_{boom}\) speed. Given similar water density across wide region, lightning can propagate from end to end.
The waiting factor is for condensed water in the clouds to be at the right density of \(971.8\,kgm^{-3}\).
Goodnight.
