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The work function is typically related to the photoelectric effect where photons hit a solid metal and if the energy of a photon is higher than the work function, then the electrons are ejected from the metal. For ionization energy, the energy is related to the energy required to remove an electron from any element in the gas state, and is typically used with bonding.
In the lecture, Dr. Lavelle explained that ionization energy is the energy needed to remove an electron from an atom in the gas phase, while the threshold energy (work function) is the energy required to remove an electron from a solid. Hope that helps!
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