|MadSci Network: Physics|
Electrons of hydrogen atoms can indeed absorb photons of energy greater than the minimum ionizaton energy of 13.6eV; the excess appears as kinetic energy of the now-freed electron (and possibly the proton as well, via recoil. Energetic enough photons, many MeV, as found in the cores of heavy stars, can even photodisintegrate atomic nuclei). In this sense, photon absorption by a single hydrogen atom is exactly analagous to the photoelectric effect in that any energetic-enough photon will free one electron. What hydrogen can not do is absorb at all energies below 13.6eV, but only at certain specific energies equal to the difference in allowed energy levels for the electrons.
The energy necessary to yank an electron out of a solid (by whatever means, photon irradiation being one) tends to be related to the ionization energy of the atoms of which the solid is made. That is, easily ionized atoms such as sodium tend to be solids that have low work functions (the minimum energy necessary to pull an electron from a piece of electrically neutral solid), But this isn't exact; atoms being close enough together to make solids affects the internal electron energies, especially when compounds (as opposed to single elements) get involved.
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