When Cold Is Not

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.