# Electron mobility

Discussion in 'Homework Help' started by jnp, Apr 25, 2008.

1. ### jnp Thread Starter New Member

Apr 25, 2008
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0
hi i have a question re mobility of electrons in copper. i've been given the conductivity and resistance. how do i find the mobility? all the formulas I've tried to find require the density of free electrons and i'm stuck because i don't have voltage or temperature.
cheers
j

2. ### Dave Retired Moderator

Nov 17, 2003
6,960
171
They have given you the resistance of the copper right? This resistance will be at a particular temperature, therefore you need to find a table of the resistance (not resistivity, because from your question you do not have physical information about your wire to reduce your resistance to resistivity) of copper as a function of temperature - therefore you now have the temperature.

What are the equations you have come across? (We can have a look at the other unknowns you have).

Dave

3. ### jnp Thread Starter New Member

Apr 25, 2008
4
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thanks dave, i started with :
question: copper has 1 outer electron. copper has 8.5 x 10^22 atoms/cm^3 and conductivity of 5.8 x 10^5 S/cm. Resistance is 1.7x10^-6 ohms. I found that temp is at 25 degrees C.
I have to find the mobility (mu) of the conduction electrons.

i started with conductivity x Electrical field = J
Jn = n x mu(n) x E x q
therefore, conductivity must be n x mu(n) q
given q = 1.6x10-19, but i can't find n.
being that they are talking about intrinsic copper, n = BT^3/2 x e ^(-Eg/2kT)
I can't find Eg or B. Am I heading in the wrong direction? The question is listed under intrinsic semiconductors, but Copper is a conductor. I'm confused! Perhaps there is a simpler way?
Cheers
J

4. ### jnp Thread Starter New Member

Apr 25, 2008
4
0
basically, i think i need the carrier concentration of intrinsic copper at 25 degrees C.
Unless there is an easier solution.

5. ### jnp Thread Starter New Member

Apr 25, 2008
4
0
the fact that the question mentions that copper has 29 electrons/atom and 28 in inner shells and 1 in shell 4, which gives copper its conductivity of 5.8x10^5 S/cm.

I feel like i'm missing something here. is there a way of finding the concentration just from this? i'm not sure if i have been going in the right direction

6. ### Papabravo Expert

Feb 24, 2006
12,210
2,697
If you take the Atomic Weight, Avagodro's number, and the density of copper you should be able to take a stab at it, but don't you require an Electric Field to generate the drift velocity?

According to wiki it is 1.0 (m^2/V*s) @300 degrees K

7. ### jpanhalt Expert

Jan 18, 2008
7,533
1,806
I've done that calculation. Problem was I didn't know how many electrons per atom were involved in conduction. Or, is it electrons per unit crystal lattice, etc.? I don't know, but would sure like to. John

8. ### Papabravo Expert

Feb 24, 2006
12,210
2,697
It is the single electron in the incomplete shell. The other 28 are bound so tightly to the nucleus that it would take an extraordinary amount of energy to break them free.

9. ### jpanhalt Expert

Jan 18, 2008
7,533
1,806
Well, yes and no. Some of the remaining 28 electrons are lost quite readily in formation of chemical compounds. The listed valences of copper are +1, +2, +3, and +4, and compounds with +1 and +2 are very common. Examples are copper sulfate (+2), copper oxides (+1 and +2), etc. In fact, the +2 state is extremely stable.

Of course, comparing energy levels of valence electrons with conduction in metals is not all that straight forward. I had read the hyperphysics article quite awhile ago (http://hyperphysics.phy-astr.gsu.edu/hbase/electric/ohmmic.html). That article states in reference to conductors, "This can be seen to be a result of their valence electrons being essentially free. In the band theory, this is depicted as an overlap of the valence band and the conduction band so that at least a fraction of the valence electrons can move through the material." (emphasis added)

My uncertainty was basically about what was the fraction. The hyperphysics site continues on to calculate the maximum conductivity of copper is 5900A/cm^2 . There is an edit from a Dr. Ma who points out that the accepted value is 400 A/cm^2. That ratio struck me a being very close to the number of atomic centers (14 centers, 4 atoms per cell) in a face-centered cubic lattice (i.e., crystal structure of copper, Wikipedia).

Now, although every copper atom might contribute to conduction by yielding one electron, it appears that empirically at room temperature the current capacity of copper is substantially less than predicted by that model. That was the reason I posited that the drift velocity may be greater than predicted by the simple model, because fewer than the theoretical number of electrons might be involved.

For the time being, I will just assume it is one-to-one and not worry about why the ampere capacity is so low. Maybe some of the experiments with quantum entanglement will allow physicists in the future effectively to label an electron, put it in a wire, and see how long it really takes to come out.

John