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From Wikipedia:

The ionization energy (IE) is qualitatively defined as the amount of energy required to remove the most loosely bound electron of an isolated gaseous atom to form a cation.

and:

Work function is the energy required to strip an electron from a solid to just outside its surface.

Then why the first ionization energy is not identical to the work function? (there is roughly a factor of 1.5 between the two quantities)

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For condensed matter the important value is the Fermi energy; this depends upon the material structure, and is a many body problem.

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  • $\begingroup$ This is the right answer but perhaps you could explain to the OP what is the Fermi sea… $\endgroup$ – user154997 Jun 5 '17 at 9:40

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