It seems to suggest that temperature of a material is centered around the nucleus as the mass of a electron is 0.00054386 times the mass of a proton, and the nucleus also has a higher concentration of charges. That would suggest temperature is a function of mass, \(m\) and charge, \(q\)
\(T=f(m, q)\)
This is consistent with the post "Hot Topic, Mumble and Jumble...", where temperature was postulated as rotational kinetic energies about the time dimensions, but this is not conclusive evidence. From that post,
\(T^2=\cfrac{1}{4}(q^2v^4_{rc}+m^2v^4_{rg})\)
\(T=\sqrt{\cfrac{1}{4}(q^2v^4_{rc}+m^2v^4_{rg})}\)
both mass, \(m\) and charge, \(q\) contributes to temperature.
Electron and proton have equal but opposite charge, however the significant discrepancy in mass and charge still suggest that most of the thermal energy is concentrated at the nucleus. Furthermore, assuming that the thermal energy of a body, \(T\) is just the statistical sum of all temperature possessed by the protons and electrons in the body.
\(T=\sum^{all}_i{ \{T_{e}\}_i} + \sum^{all}_j{\{T_{p}\}_j}\)
where \(T_{e}\) and \(T_{p}\) are the temperature of electron and proton respectively,
\(T_e=\sqrt{\cfrac{1}{4}(q^2v^4_{rc}+m^2_ev^4_{rg\,e})}\)
\(T_p=\sqrt{\cfrac{1}{4}(q^2v^4_{rc}+m^2_pv^4_{rg\,p})}\)
Obviously, \(T_e\ne T_p\ne T\). But we can formulate, \(T_{atom}\) as,
\(T_{atom}=n(T_e+T_p)\)
where \(n\) is the atomic number.
If we admit the existence of neutrons in the nucleus of an atom, \(T_n\),
\(T_n=\sqrt{\cfrac{1}{4}m^2_nv^4_{rg\,n}}\)
since neutrons have no charge, \(q=0\).
\(T_{atom}=n(T_e+T_p)+(N-n).T_n\)
where \(N\) is the mass number.
\(T_{atom}=nT_e+n.T_p+(N-n).T_n\)
\(T_{nucleus}=n.T_p+(N-n).T_n\)
\(T_{atom}=nT_e+T_{nucleus}\)
If the discrepancies in mass is more significant, (given the relative values of charge and mass, charge is more significant)
\(T_{atom}\approx T_{nucleus}\)
Then the total thermal energy of a body, at temperature \(T\) is,
\(T=\sum^{all}_i{ \{T_{atom}\}_i}\approx \sum^{all}_i{ \{T_{nucleus}\}_i}\)
What is more important is that \(T_{nucleus}>T_e\), as such a temperature gradient exist between the nucleus and the orbiting electrons.
Since \(T_e\) is not dependent on \(r_e\), \(T_e\) remains constant as \(r_{e2}\) is decreased to \(r_{e1}\), and the whole temperature profile shifts accordingly as illustrated above. This is the origin of the temperature gradient postulated in the post "Band Gap? Just A Kink". It is just the temperature of the body distributed uniformly among its constituent atoms. This temperature is concentrated at the nucleus because of the relative large mass and a concentration of positive charge there. Temperature here is defined as energy. It is noted that there are other electrons below the valence electrons.
However, since \(m\) and \(q\) are not normalized properly, that is to say there is no equivalence relationship between the two, \(m\) is not compatible with \(q\). We cannot simply further.
We want,
\(m=h(q)\) or \(q=f(m)\) somehow.
