Question

The first allowed excited state of a hydrogen atom is 10.2 eV above its lowest energy (ground) state. To what temperature should hydrogen gas be raised so that inelastic collisions may excite an appreciable number of atoms to their first excited state.

• A.
• B.
• C.
• D.

Answer 1

The correct option is B

Let T be the required temperature.
Average Energy of each atom = $\frac{3}{2}kT$
This must be 10.2 eV.
$\therefore \frac{3}{2}kT=10.2\times 1.6\times {10}^{-19}$
$(\Theta 1eV=1.6\times {10}^{-19}J)$
or $T=\frac{2\times 10.2\times 1.6\times {10}^{-19}}{3\times 1.38\times {10}^{-23}}=7.88\times {10}^{4}K$