Metal work function

[McCrunchy]

There's a thing I don't get about the electron work function of a metal:

in this wikipedia article, they say it's the difference between the bottom of the image-charge potential and the fermi level (just look at the picture in the article). But the image-charge potential has no bottom - it goes as 1/a, a being the distance between the electron and the metal surface . How do you get around that ? Does one have to reach for quantum mechanics to get a bottom - just as when solving for the hydrogen atom's energy levels ? If so, how did the likes of Einstein do to compute a work function before ~1915 ?

 

Thanks in advance for your help,

 

McCrunch

[gokul.er137]

work function of a metal to the best of my knowledge refers to the work that has to be done in order to remove a valence electron from the metal atom. Essentially, the energy absorbed by the electron must be such that it is at least a bit more larger than the work function. As a basic relation - > E = hc/lambda, the only variable is lambda. As this directly depends upon frequency, you hence need a minimum frequency (threshold frequency) in order to excite the electron from its valence orbit. This frequency of light absorbed by the electron must give it energy greater than threshold frequency. I suppose that is all there is to it.

 

To calculate the energy levels of hydrogen you can use this formula ->

1/lambda = R(1/n1^2 - 1/n2^2) where R - > Rydberg constant

lambda - > wavelength of light

n1 an n2 represent the orbits of the hydrogen for which the electron "jump" is taking place.

Edited July 15, 2009 by gokul.er137