Method of Images: Find Minimum Energy for Electron to Escape Metal Surface

[bon]

Homework Statement

A point charge +q is initially at distance x from a conducting plane of infinite extent and held at zero potential. Find the work done in moving the charge to an infinite distance from the plane. Hence find the minimum energy an electron must have in order to escape
from a metal surface (assume that it starts at a distance 0.1nm, which is about one atomic diameter, from it). Express your answer in electron-volts.
[Answers: q^2/(16πε0x) ; 3.6eV]

Homework Equations

The Attempt at a Solution

So I've worked out the work done and found this to be q^2/[16pi ε d] as required.

just not sure how to work out the minimum energy the electron in the surface must have to escape. don't see how this relates to the previous part. any help please? Thank you :)

 

[bon]

any ideas?

 

[gneill]

Presumably kicking an electron off the surface with enough kinetic energy to escape is equivalent to the work required to move an equivalent charge to infinity (that is sort of the defining characteristic of "escape velocity").

So if you plug in the fundamental charge and the given distance into your formula, and convert the result to electron volts, you should be golden.

 

[bon]

Thanks but it's not clear to me how the two situations are the same. The first involves taking the charge q and moving it away from the conducting plate. The second involves leaving the plate and charge where they are and taking an electron from inside the plate... :S

 

[gneill]

If your charge q was -q instead, would that make any difference to the work you computed?

 

[bon]

no but that wasn't what i meant.in the first case the conducting plate is fixed, while the charge q is taken off to infinity..

in the second case, the conducting plate AND the charge q is fixed while the electron is moved off to infinity..

 

[gneill]

I think we've got different interpretations of what the q represents.

In my mind, the q is the electron with its charge -e. It's been booted off the surface of the metal by an incoming photon and given some KE. Because the surface is held at constant zero potential (I suppose that it's grounded in some way), the +e charge "hole" that the electron made when it left is quickly filled by a conduction electron and the plate remains neutral.

Now the situation is analogous to removing a charge q (in this case q = -e) from the vicinity of the plate to infinity, where the KE given to the electron provides the energy to accomplish the work.

 

[bon]

sorry - yes- id misread the question! Thank you so much"_)