If a hydrogen atom in the ground state absorbs a photon of energy 12.09 ev, to which state will the electron make a transition?

The energy levels of the hydrogen atom are given by
(1)
where n is the level number. Therefore, the ground state has energy of


If the atom absorbs a photon of energy , the final energy of the hydrogen atom is


And we can use eq.(1) to find the corresponding level number:

So, the electron made a transition to the n=3 level.