Question

Can a hydrogen atom absorb a photon having energy more than 13.6 eV ?

Answer 1

Yes, because When an electron absorbs a photon it gains the energy of the photon. Because an electron bound to an atom can only have certain energies the electron can only absorb photons of certain energies. For example, an electron in the ground state has an energy of -13.6 eV. The second energy level is -3.4 eV. Thus it would take $E2-E1=-3.4eV-(-13.6)eV=10.2eV$ to excite the electron from the ground state to the first excited state.

If a photon has more energy than the binding energy of the electron then the photon will free the electron from the atom – ionizing it. The ground state is the most bound state and therefore takes the most energy to ionize.