# Homework Help: Mean Free Time Silicon (PURCELL 4.12)

1. Oct 3, 2012

### NullSpace0

1. The problem statement, all variables and given/known data
This is Purcell 4.12... Given that conductivity in silicon at 500K is 0.3 sec-1, deduce the mean free time between collisions of an electron.

2. Relevant equations
Electron mass is 9.1x10-28 grams (mass of a hole is exactly the same), the charge on an electron is 4.8x10-10, the density of electrons and holes is each 1015.

3. The attempt at a solution
I solved Purcell's equation for conductivity to find mean free time instead:

T=(Mass*σ)/(2Ne2)... and I get something like 5.92x10-25 seconds. Isn't this way too small? Or did I do something wrong?

2. Oct 6, 2012

### schaefera

Are you sure that the holes count as mobile? What is their mass? Would counting them effectively halve the time you're looking for?

3. Oct 6, 2012

### TSny

According to page 147 of Purcell, the conductivity of pure silicon at 500 K is 0.3 (ohm-cm)-1 rather than 0.3 sec-1.

4. Oct 7, 2012

### schaefera

Ah! So the OP's problem was conversion.

What about that factor of 2?

5. Oct 7, 2012

### TSny

I believe the factor of 2 is there because an electron could collide with either another electron or a hole. So, the number density of particles that the electron could collide with would be twice that of just the number density of electrons alone.