Can a photon with energy value not corresponding to the discrete energy level differences excite an atom? [duplicate]

Question

I'm a sophomore majoring in physics, and I had some question about the discrete energy value of atoms and its excitation.

So, I know that in order to make a hydrogen atom in a ground state to get "excited" to its 1st excited state we need 10.2eV. For 2nd excited state, we need 12.1eV.

My question is this: Will a photon with the energy value 11eV excite the hydrogen atom? Or will it just provide no energy to the atom and go away?

Also, if I "shoot" a photon with the energy 12.1eV to the atom, will it get excited to its 2nd excited state? Or is there any possibility the atom will be excited to its 1st excited state?

If the atom can be excited to either the 1st or the 2nd excited state, are the possibilities the same?

Answer 1

If the incoming photon has an energy exactly equal to the difference between the two electron energy levels, it can be absorbed and the electron in the lower energy level will jump to a higher energy level. Otherwise, the photon will not be absorbed and scatter.

An photon of intermediate energy will never excite an electron to a higher energy level. It needs to have an energy $$h\nu=\Delta E=E_2-E_1$$ where $E_2$ and $E_1$ correspond to different energy levels, and so an energy "in between" will cause no excitation to another level.

An absorbed photon with energy equal to the difference between the second level and ground state, will not promote an electron to the first level either. Again, in this instance, the electron may leap from the ground state to the second energy level but never to the first if the incoming photon is completely absorbed.

Also note that incoming photons can also have sufficient energy to liberate the electron (or cause ionization) from the atom completely. See photoelectric effect.