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