A 12 . 5eV electron beam is used to bombard gaseous hydrogen at...

According to Bohr's postulates, if an electron absorbs a photon with energy equal to the difference between the energies of an excited state and the ground state, it will jump to a higher energy orbital.

Considering that the energy of the colliding electron is $10 . 2eV$ or $12 . 09eV$, depending on how much energy is lost during the collision. $n = 3$ is the maximum excited state. Hence, there are spectral lines in a total of

$\begin{cases}C2 3 & = & \dfrac{3 !}{2 ! 1 !} \\ & = & 3\end{cases}$