At a temperature T , the average kinetic energy of gas molecules is...

The binding energy of a hydrogen atom is $13.6 \text{ eV}$.

The average kinetic energy of a gas molecule is given as $1.5 kT$.

Equating the average kinetic energy to the binding energy of the hydrogen atom:

$1.5 kT = 13.6 \text{ eV}$

Substituting the value of the Boltzmann constant $k = 8.62 \times 10^{-5} \text{ eV K}^{-1}$:

$1.5 \times 8.62 \times 10^{-5} \times T = 13.6$

$1.293 \times 10^{-4} \times T = 13.6$

$T = \dfrac{13.6}{1.293 \times 10^{-4}} \approx 1.05 \times 10^5 \text{ K}$

At this extremely high temperature, the average kinetic energy of the molecules ($13.6 \text{ eV}$) is much greater than the bond dissociation energy of a hydrogen molecule (which is approximately $4.5 \text{ eV}$).

As a result, the violent collisions between molecules will cause them to dissociate into individual atoms. Therefore, hydrogen will not remain in molecular form.