Question

What happens when suppose an electron in H atom absorbs energy of 3.8eV (3.4 being the energy difference between ground and 1st excited state)?

Answer 1

the electron will cease to be bound to the atom, and the atom will become ionised?

Answer 2

The ionization energy of hydrogen is 13.6 ev so 3.8 ev will excite the hydrogen atom to a state that will absorb that exact energy if it exists. if not I suppose it could also absorb 3.4 ev to raise the energy of the atom to the first excited state and radiate the remaining 0.4 ev as a photon in the UV range.