Work function of electrons in a metal

[SQUB]

Homework Statement

Neglecting quantum effects, estimate the work function of a metal which consists of equivalent atoms arranged in a cubic lattice with a lattice constant a.
--> Show that the method of images fails at small distances.
--> Solve the problem, assuming that the electron approaches the crystal along the line perpendicular to the (100) surface, which passes through the middle of a face formed by four nearest-neighbor ions. For simplicity, neglect the effect of all other ions.

Relevant Equations

Ek=hf-ϕ

Hi everyone, I have to solve this homework without having any books where to find the theroical topic or examples, so if you could help me find materials that I can use to understand or you want to try help me understand how to get the solution would be very helpfull. I don't have enough time to read a long discussion about this topic before doing the assigment but if you send me also those I will defintly read them before the exam :) .
Things I think I have understood:
-the work function is the minimum energy required to extract one electron from a metal
-the electron's gain of kinetic energy (Ek) is the difference between incident photon energy (hf) and work function of the metal (ϕ)
-if i know the threshold frequency of the metal (f0) obviously I can write ϕ=h*f0Some questions:
-Is the "method of image" the method of image charges that for example can be used to find the field of a charge near a conducting surface?
- What is the (100) surface ?Lots of karma to everyone who want to help!

 

[BvU]

if i know the threshold frequency of the metal (f0) obviously I can write ϕ=h*f0

Yes, but you don't: they don't tell you what metal it is. Finding (estimating) a potential is the core object of the exercise

-Is the "method of image" the method of image charges that for example can be used to find the field of a charge near a conducting surface?

Yes

- What is the (100) surface ?

See Miller index. The yz plane.

Small disclaimer :Like you, I look at this exercise as a beginner (whatever was taught to me half a century ago -- in undergraduate physics -- is gone for lack of use). So for what it's worth:
Suppose you have four charges +e/4 on corners of a square and one charge -e in the center. The exercise is to calculate how much energy is needed to pull the +e straight up to infinity .

If I'm not wrong (and the good thing about PF is that correction will always follow if you are wrong ), then I surely find this a very nice exercise.

$\mathstrut$

 

[SQUB]

Yes

And why should I not be able to use this kind of method? I actually would not think about it because it seems not a useful way to resolve the problem but it's not possible to use it because there is more than one charge? If there are multiple charges, can't we simply construct an image charge for each of them (and maybe use superposition)?

See Miller index. The yz plane.

Nice! Thank youI will try to calculate the energy in this way, I'll let you know!

 

[SQUB]

So I have computate the value of the work function (but it seems too small at first look), but I still don't know why this method will fail for the short distance. I think it could have relation with the fact that the potential on the surface has to be the same everywhere but I'm not shure it's enough as explanation...