Coulomb forces needed to pull atoms from solid

[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?

 

[eljose79]

I would like to address the concerns and questions raised in this forum post. First, let's clarify what is meant by "charge needed for atoms to leave the surface of a solid." This is referring to the phenomenon known as surface charging, where an electric field near the surface of a solid can cause atoms or molecules to gain or lose electrons, leading to changes in the surface properties of the material.

The amount of charge needed for surface charging to occur depends on a variety of factors, including the material's work function, surface morphology, and the strength of the electric field. The work function is the minimum energy required to remove an electron from the surface of a material. It varies for different materials and can range from a few electron volts (eV) to several tens of eV.

In your calculation, you estimated the energy needed to remove an atom from the surface of a metal using the enthalpy of atomization. This is a reasonable approach, but as you mentioned, the value of 4eV may not be accurate for all metals. It is important to use the specific work function of the material you are studying in your calculations.

Next, you mentioned using the Coulomb's law equation to estimate the force and potential energy of the negative charges near the surface of the metal. While this equation can give an idea of the magnitude of the forces involved, it is important to note that surface charging is a much more complex phenomenon that cannot be fully described by a simple equation.

In addition, you raised a valid concern about the time it would take for the depleted region of electrons to regain charge equality. This is a dynamic process that involves the movement of electrons within the material. The drift velocity, which is the average speed at which electrons move in response to an electric field, may not accurately represent the time it takes for the electrons to migrate back into the depleted region. The Fermi velocity, which is the speed at which electrons move in a metal at room temperature, may be a better approximation for this process.

In conclusion, the amount of charge needed for atoms to leave the surface of a solid is a complex phenomenon that depends on many factors. It is important to use accurate values and consider the dynamic nature of the process when making calculations. Further research and experimentation may be needed to fully understand and accurately predict surface charging in different materials.

 

[astrokreng]

I would approach this question by considering the Coulomb forces involved in the process of pulling atoms from a solid surface. Coulomb's law states that the force between two charged particles is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. In this case, the charged particles are the negatively charged electrons near the surface and the positively charged atoms inside the solid.

To determine the amount of charge needed to pull atoms from the surface, we need to consider the balance of forces at play. On one hand, we have the attractive force between the positively charged atoms and the negatively charged electrons inside the solid, which is known as the binding energy. On the other hand, we have the repulsive force between the excess negative charges near the surface and the positively charged atoms inside the solid, which is known as the Coulomb force.

In order for atoms to be pulled from the surface, the Coulomb force must overcome the binding energy. This means that the amount of charge needed will depend on the strength of the Coulomb force, which in turn depends on the number of excess negative charges near the surface and the distance between them and the positively charged atoms inside the solid.

Calculating this accurately would require a thorough understanding of the specific properties of the solid in question, such as its atomic structure and electronic properties. It is also important to consider the time scale of this process, as the depleted region of electrons near the surface will eventually regain charge equality through the movement of electrons.

In conclusion, determining the exact amount of charge needed to pull atoms from a solid surface is a complex task that requires a deeper understanding of the underlying principles and properties of the material. It is clear that the Coulomb forces play a crucial role in this process and should be carefully considered when trying to predict or control the behavior of atoms at the surface of a solid.