Hydrogen Plasma At $T_c$

From the post "High Temperature Requires Thick Skin, Very Thick Skin",

$T^{ 2 }_{ c }=\cfrac { (m_{ e }+m_{ p })^{ 2 } }{ m_{ e }m_{ p } } \cfrac { q^{ 2 } }{ \varepsilon _{ o } } { \tau _{ o } }$

If we were to use

$\tau_o$ = 6.486e13

For one hydrogen atom,

$T_c$ = (( 9.10938e-31+1.67262e-27)^2/( 9.10938e-31*1.67262e-27)*(1.602176565e-19)^2/8.8541878176e-12*6.486e13)^(1/2)=1.859e-5 J.

$T_c\approx$ 1.160e14 eV

This is the temperature that hydrogen form plasma readily, where  $r_e=0$  is a valid solution to the quadratic equation for  $r_e$.  This value is still high.

No comments,  $\tau_o$  is still the new kid in town.