How Do You Calculate Electron Mobility in Copper?

[Staudinger]

Hey all,

I have a pretty straightforward question about electron mobility in metals. We are given the length of a copper wire, it's radius, the current flowing through it, voltage drop across it, and the proportion of free electrons to copper atoms. I've found the current density, conductivity, resistance and resistivity of the wire, but I can't figure out how to calculate the electron mobility. We were given a few equations, one of which was specifically for metals,

$$\sigma$$ = $$n_{e}\mu_{e}$$

in which
$$\sigma$$ is conductivity
q is the charge of an electron
$$\mu_{e}$$ is the the mobility of electrons
$$n_{e}$$ is the density of free electrons

My problem is that I don't know how to translate the proportion of free electrons to copper atoms correctly. I tried using the ratio, which came out much too high, something like 10^24. We are not given the density of copper atoms in the wire, but I can find it in an appendix. Would it make sense to figure out how many copper electrons are in a cubic cm, and use that to find the density of free electrons?

Any help would be greatly appreciated, I feel as though I'm missing out on the aha! moment that would pull this all together.

Thanks!
Staudy

 

[Shooting Star]

There is one free electron to one copper atom, if that's what's stopping you.

Why don't you just write down your calculations. It can't be very long.

 

[ogb p]

Hello Staudy,

Calculating electron mobility in copper involves understanding the relationship between the density of free electrons and the density of copper atoms in the wire. The ratio of free electrons to copper atoms is typically very small, on the order of 10^-6. This means that for every million copper atoms, there is only one free electron available for conduction.

To calculate electron mobility, you can use the formula you mentioned, \sigma = n_{e}\mu_{e}. However, instead of using the ratio of free electrons to copper atoms, you should use the actual density of free electrons in the wire. This can be calculated by multiplying the density of copper atoms by the proportion of free electrons to copper atoms. As you suggested, you can find the density of copper atoms in an appendix or by doing some research.

Once you have the density of free electrons, you can rearrange the equation to solve for electron mobility, \mu_{e} = \sigma / n_{e}. This will give you the mobility of electrons in units of meters squared per volt-second (m^2/Vs).

I hope this helps and leads you to your "aha!" moment. Keep up the good work!

Best,