From the previous post "Hot Topic, Less Mumble, Jumble...",
\(T=\cfrac{1}{2}(qv^2_{rc}+mv^2_{rg})\)
then for an electron, its temperature is given by,
\(T_e=\cfrac{1}{2}(qv^2_{rc}+m_ev^2_{rg\,e})\)
and for a proton,
\(T_p=\cfrac{1}{2}(qv^2_{rc}+m_pv^2_{rg\,p})\)
and for a neutron,
\(T_n=\cfrac{1}{2}m_nv^2_{rg\,n}\)
Temperature associated with an atom is,
\(T_{atom}=n(T_e+T_p)+(N-n)T_n\)
where \(N\) is the mass number and \(n\) the atomic number,
\(T_{atom}=nT_e+nT_p+(N-n)T_n\)
Let,
\(T_{nucleus}=nT_p+(N-n)T_n\)
\(T_{atom}=nT_e+T_{nucleus}\)
And since,
\(T_e<nT_e<nT_p<nT_p+(N-n)T_n\)
\(T_e<T_{nucleus}\)
For the sake of completeness.
