Questions on electrons incident on a metal surface

[b2c3yun]

Homework Statement

Electrons with kinetic energy E are incident normally from vacuum on a metal surface. The work function of the metal is F. Calculate the fraction of electrons reflected from the surface. Neglect any temperature effects.

Homework Equations

The Attempt at a Solution

Since work function is defined as the minimal energy required to extract one electron from the metal, all the electrons with energy larger than F will be reflected.

From statistical mechanics, the so-called "electrons with kinetic energy E" are actually electrons with an energy distribution. My feeling is the this E is the average energy from this distribution. And the fraction of electrons reflected is the fraction of electrons with energy larger than F in this distribution. But I am wondering how I can get the distribution. Should I use Boltzman velocity distribution and derive the energy distribution? Or should it be a Gaussian distribution peaked at E? It never indicates the temperature in the problem, but I feel temperature should matter here.

Any help is appreciated.

 

[Jhero]

You are correct in thinking that the work function determines the minimum energy required to extract an electron from the metal surface. This means that any electrons with energy equal to or greater than the work function will be reflected from the surface.

As for the energy distribution of the incident electrons, it is important to note that the average kinetic energy, E, is not the same as the maximum kinetic energy. The maximum kinetic energy will depend on the temperature of the electrons, which is not given in the problem. Therefore, it is not necessary to consider the temperature effects in this calculation.

To determine the fraction of electrons reflected, you can use the Boltzmann velocity distribution to derive the energy distribution. This will give you a Gaussian distribution peaked at E, which is the average kinetic energy. Then, you can integrate this distribution from F to infinity to find the fraction of electrons with energy larger than F, which will be the fraction reflected from the surface.

I hope this helps. Let me know if you have any further questions.