# Coulomb forces needed to pull atoms from solid

1. Sep 1, 2008

### gareth

I'm trying to work out the amount of charge needed for atoms to leave the surface of a solid.

Here's the scenario, if we have a solid, say a metal for example, and we take some charge out of a certain area of the metal so it is just leaving the surface of the metal, we have a space charge near the surface of negative charge outside the crystal and positive inside the crystal.

How much charge is needed before atoms start to get ripped off the surface?

I tried calculating this but I'm not too confident in the answer.

This is what I did;

Estimate the energy needed to rip an atom from a solid surface, which would roughly equal the enthalpy of atomisation fro one atom, which turns out to be around 4eV for a metal (not sure about this).

Then estimate the force of a bunch of negative charges would exert on the positve ones inside the material using the q1q2/r^2 equation. Convert this to potential by multiplying by r, in this case 1nm.

But it turns out this is a huge force! And has massive potential energy, and even a relatively small number of negative charges near the surface could rip the material apart.

This is a simplistic view I admit, one of my main concerns is the time it would take for the depleted region of electrons in the metal to regain charge equality. I'm not sure should the drift velocity (mm/s) or the Fermi velocity (1e6 m/s) should be used to calculate the time taken for the electrons to migrate back into the depleted region.

Any thoughts?