# Homework Help: Protein diffusion

1. Apr 6, 2009

### superwolf

1. The problem statement, all variables and given/known data

You release a billion protein molecules at position x=0 in the middle of a narrow capillary test tube. The molecues' diffusion constant is 10^-6 cm^2s^-1. An electric field pulls the molecules to the right (larger x) with a drift velocity of 1 micrometer per second. Nevertheless, after 80 s you see that a few protein molecules are actually to the left of where you released them. How could this happen? What is the ending number density right at x=0?

2. Relevant equations

Suppose N molecules all begin at the same location in 3D space at time zero. Later the concentration is

$$c(r,t)=\frac{N}{(4 \pi Dt)^{3/2}} e^{-r^2/(4Dt)}$$

3. The attempt at a solution

From a similar problem, it looks like the formula in 1D is

$$c(r,t)=\frac{N}{(4 \pi Dt)^{1/2}} e^{-r^2/(4Dt)}$$

Is this correct?

If so, we have

$$c(0,80)=\frac{1 \cdot 10^9}{(4 \pi 1 \cdot 10^-6 \cdot 80)^{/2}} e^0 = 3.15E10 cm^-1$$

This clearly must be wrong, or what?