Question

Find the temperature at which the average kinetic energy of the molecules of hydrogen equals the binding energy of its electron in ground state, assuming average kinetic energy of hydrogen gas molecule = $\frac{3}{2}kT$

Answer 1

The binding energy of electron in the ground state is given as $E=13.6eV=13.6\times 1.6\times {10}^{-19}Joule=21.76\times {10}^{-19}Joule$

Average kinetic energy is $E=3kT/2$ both are eqaul so $T=\frac{2\times 21.76\times {10}^{-19}}{3k}=\frac{43.52\times {10}^{-19}Joule}{3\times 1.38\times {10}^{-23}Joule/Kelven}$, $k$ is Boltzman's constant.

So we get the temperature as $T=105120Kelvin$