Question

The average kinetic energy of molecules in a gas at temperature T is 1.5 kT. Find the temperature at which the average kinetic energy of the molecules of hydrogen equals the binding energy of its atoms. Will hydrogen remain in molecular form at this temperature ? Take k = 8.62 x 10^-5 eV/K.

Answer 1

KE = 3/2 KT = 1.5 KT, K = 8.62 x 10^–5 eV/k, Binding Energy = –13.6 (1/∞ – 1/1) = 13.6 eV.

According to the question, 1.5 KT = 13.6

=> 1.5x 8.62 x 10^–5 x T = 13.6

=> T= 13.6/(1.5 x 8.62 x10^-5)= 1.05 x10⁵ K

No, because the molecule exists an H₂⁺ which is impossible.