A 12.5eV electron beam is used to bombard gaseous hydrogen at room temperature. The number of spectral lines emitted will be:

The energy of the electron in the hydrogen atom's ground state (n=1) is -13.6 eV.

The electron beam has an energy of 12.5 eV. When this beam bombards the hydrogen atom, it can excite the electron to higher energy levels.

The energy levels of a hydrogen atom are given by the formula: E = -13.6/n^2 eV, where n is the principal quantum number.

The energy levels that the electron can be excited to with a 12.5 eV beam are those for which -13.6/n^2 is greater than -12.5.

Solving this inequality gives n^2 < 13.6/12.5, or n < sqrt(13.6/12.5), which gives n < 3.3.

So, the electron can be excited to the n=2 and n=3 levels.

When the electron de-excites back to the ground state, it can do so in a stepwise manner, emitting a photon at each step.

From n=3, it can go to n=2 and then n=1, or directly to n=1. This gives 2 possible transitions.

From n=2, it can only go to n=1, giving 1 possible transition.

So, the total number of spectral lines emitted is 2 + 1 = 3.