Everything about The Work Function totally explained
The
work function is the minimum
energy (usually measured in
electron volts) needed to remove an
electron from a solid to a point immediately outside the solid surface (or energy needed to move an electron from the Fermi energy level into vacuum). Here "immediately" means that the final electron position is far from the surface on the atomic scale but still close to the solid on the macroscopic scale. The work function is an important property of metals. The magnitude of the work function is usually about a half of the
ionization energy of a free atom of the metal.
Work Function and Surface Effect
Work function
W of a metal is closely related to its
Fermi energy level
yet the two quantities are not exactly the same. This is due to the surface effect of a real-world solid: a real-world solid isn't infinitely extended with electrons and ions repeatedly filling every
primitive cell over all
Bravais lattice sites. Neither can one simply take a set of Bravais lattice sites
where
, the Richardson constant, is a specific material constant. The current density increases rapidly with temperature and decreases exponentially with the work function. Changes of the work function can be easily determined by applying a retarding potential
between the sample and the electron emitter;
is replaced by
in above equation. The difference in the retarding potential measured at constant current is equivalent to the work function change, assuming that the work function and the temperature of the emitter is constant.
One can use the Richardson–Dushman equation directly to determine the work function by temperature variation of the sample, as well. Rearranging the equation yields
. The line produced by plotting
vs.
will have a slope of
allowing to determine the work function of the sample.
Electron Work Functions of The Elements
Units: eV electron Volts
reference: CRC handbook on Chemistry and Physics.
Note: Work function can change for crystaline elements based upon the orientation. For example Ag:4.26, Ag(110):4.64, Ag(110):4.52, Ag(111):4.74
| Element |
eV |
Element |
eV |
Element |
eV |
Element |
eV |
Element |
eV |
Element |
eV |
| Ag |
4.26 |
Al |
4.28 |
As |
3.75 |
Au |
5.1 |
B |
4.45 |
Ba |
2.7 |
| Be |
4.98 |
Bi |
4.22 |
C |
5 |
Ca |
2.87 |
Cd |
4.22 |
Ce |
2.9 |
| Co |
5 |
Cr |
4.5 |
Cs |
2.14 |
Cu |
4.65 |
Eu |
2.5 |
Fe |
4.5 |
| Ga |
4.2 |
Gd |
3.1 |
Hf |
3.9 |
Hg |
4.49 |
In |
4.12 |
Ir |
5.27 |
| K |
2.3 |
La |
3.5 |
Li |
2.9 |
Lu |
3.3 |
Mg |
3.66 |
Mn |
4.1 |
| Mo |
4.6 |
Na |
2.75 |
Nb |
4.3 |
Nd |
3.2 |
Ni |
5.15 |
Os |
4.83 |
| Pb |
4.25 |
Pt |
5.65 |
Rb |
2.16 |
Re |
4.96 |
Rh |
4.98 |
Ru |
4.71 |
| Sb |
4.55 |
Sc |
3.5 |
Se |
5.9 |
Si |
4.85 |
Sm |
2.7 |
Sn |
4.42 |
| Sr |
2.59 |
Ta |
4.25 |
Tb |
3 |
Te |
4.95 |
Th |
3.4 |
Ti |
4.33 |
| Tl |
3.84 |
U |
3.63 |
V |
4.3 |
W |
4.55 |
Y |
3.1 |
Zn |
4.33 |
| Zr |
4.05 |
|
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