From the post "Cold Temperature Requires Thick Skin, Very Thick Too",
\( T^{ 2 }_{ c }=4\pi \tau _{ o }\cfrac { (m_{ e }+m_{ p })^{ 2 } } { m_{ e }m_{ p } }(\cfrac { q^{ 2 } }{ 4\pi \varepsilon _{ o } } -\cfrac { 1 }{ 2 } m_{ e }v^{ 2 }r_{ e })\)
If we were to use \(r_{pe}\) = 3.41e-15 and \(\tau_o\) = 6.486e13
\(T^2_c\approx\)4*pi*6.486e13*( 9.10938e-31+1.67262e-27)^2/( 9.10938e-31*1.67262e-27)*((1.602176565e-19)^2/(4*pi*8.8541878176e-12)-1/2*9.10938291e-31*(2^(1/2)*299792458)^2*3.41e-15)
\(T^2_c\approx\)-7.262e-11 < 0
Hydrogen has no double root.
