Calculating Collision Frequency of Electrons in Copper Cube

[hnnhcmmngs]

Homework Statement

Verify the claim of Section 7.2 that the electrons of a metal collide with the surface at a rate of about 10^30 per second per square centimeter. Do this by estimating the collision frequency of electrons in a 1.00-cm cube of copper metal with one face of the cube surface. Assume that each copper atom contributes one conduction electron to the metal (the chemical valence of copper is 􏰄1) and that these conduction electrons move freely with kinetic energy equal to 7.00 eV.

Relevant Equations

I don't know which equations are relevant for this question.

Homework Statement: Verify the claim of Section 7.2 that the electrons of a metal collide with the surface at a rate of about 10^30 per second per square centimeter. Do this by estimating the collision frequency of electrons in a 1.00-cm cube of copper metal with one face of the cube surface. Assume that each copper atom contributes one conduction electron to the metal (the chemical valence of copper is 􏰄1) and that these conduction electrons move freely with kinetic energy equal to 7.00 eV.
Homework Equations: I don't know which equations are relevant for this question.

First, I just determined the number of electrons per cm^3 knowing the density of copper is 8.95 g.cm^3.
n = 6.02 * 10^23 atoms/mol * 8.95 g/cm^3 * 1 mol/63.5 g = 8.48 * 10^23 electrons/cm^3
I also determined the speed of each electron.
v = sqrt(2E/M) = 1.57 * 10^6 m/s
I just don't know how to proceed from here. Any help would be appreciated!

 

[collinsmark]

Homework Statement: Verify the claim of Section 7.2 that the electrons of a metal collide with the surface at a rate of about 10^30 per second per square centimeter. Do this by estimating the collision frequency of electrons in a 1.00-cm cube of copper metal with one face of the cube surface. Assume that each copper atom contributes one conduction electron to the metal (the chemical valence of copper is 􏰄1) and that these conduction electrons move freely with kinetic energy equal to 7.00 eV.
Homework Equations: I don't know which equations are relevant for this question.

Homework Statement: Verify the claim of Section 7.2 that the electrons of a metal collide with the surface at a rate of about 10^30 per second per square centimeter. Do this by estimating the collision frequency of electrons in a 1.00-cm cube of copper metal with one face of the cube surface. Assume that each copper atom contributes one conduction electron to the metal (the chemical valence of copper is 􏰄1) and that these conduction electrons move freely with kinetic energy equal to 7.00 eV.
Homework Equations: I don't know which equations are relevant for this question.

First, I just determined the number of electrons per cm^3 knowing the density of copper is 8.95 g.cm^3.
n = 6.02 * 10^23 atoms/mol * 8.95 g/cm^3 * 1 mol/63.5 g = 8.48 * 10^23 electrons/cm^3

I think you might be off by 1 order of magnitude there. You might want to double check your exponents.

I also determined the speed of each electron.
v = sqrt(2E/M) = 1.57 * 10^6 m/s
I just don't know how to proceed from here. Any help would be appreciated!

Given your velocity calculation, how long would it take for a single electron to travel in a cube of 1 cm length, from one side to the other, if it just moves freely?

Or better yet, since you're only supposed to consider a single side, how long would it take for the round trip: where it starts at one side, bounces off the opposite side, and then returns to the original side?

 

[Abhishek11235]

Well the answer varies as it depends on what "level" you have reached. A crude treatment gives answer as $1/6×n×v$ which on refining gives $1/4×n×v$. If you treat electron as Fermi Dirac gas,then the answer is to evaluate partition function and use partition function(See Reif, Fundamentals of Statistical And Thermal Physics)