Work function and ionization energy

[tenchotomic]

Why is it that the energy required to pull an electron out of a metal surface(work function) is approximately half of the energy required to pull an electron out of the free atom(ionization energy) of the same metal (or element)?
Is there any formula relating the two quantities?

 

[Drakkith]

I think it is because in a metal lattice there are already free electrons moving around everywhere. Pulling one of these out is much easier than a free atom which has it's electrons bound. In effect, the metallic bonds make it easier because they "share" electrons.

 

[ZapperZ]

Why is it that the energy required to pull an electron out of a metal surface(work function) is approximately half of the energy required to pull an electron out of the free atom(ionization energy) of the same metal (or element)?
Is there any formula relating the two quantities?

This is exactly the reason why a solid is not the same as an isolated atom. The formation of a solid means that the valence shell of the atoms have overlapped with more than one other atom, causing hybridization, etc. The formation of conduction band, valence band, band gap, etc. are all COLLECTIVE effects due to the all the atoms, not just one.

BTW, there's no significance to the "approximately half" value of the work function.

Zz.