# Qvasi Temperature of H

Suppose two hydrogen atoms, both initially in their ground state, are accelerated up to high speed and then collide head on. Assume that all of the kinetic energy goes into exciting the atoms (b) To what temperature would you need to heat hydrogen gas to make this collision likely?

The radius of hydrogen atom is $R = 0.53*10^{-10} m$

The charge of Hydrogen nucleus is $Q = +e =1.6*10^{-19} C$

The potential energy at distance 2R (collision of atoms) is

$E_p = e*U = e*(K*e)/(2R) = (1.6*10^{-19})^2*9*10^9/(2*0.53*10^{-10}) =2.173*10^{-18} J$

kinetic energy for 2 atoms is $E_c =2*m v^2/2$

$v = \sqrt{(E_c/m)} = 1.545*10^6 m/s$

b)

In the kinetic theory

$V_{rms}^2 = 3RT/M$

M = 1 for hydrogen (molecular mass) and R = 8.31,

$T = M*V^2/3R = 9.58*10^{10} K$