Diffusion vs. Size: Exploring Eq. 4.14

[superwolf]

Homework Statement

Eq. 4.14:

[tex]
\zeta = 6 \pi \eta R
[/tex] (Stokes formula)

2. The attempt at a solution

In my plot, collagen, hemoglobin and lactoglobulin give a straight line, while ribonuclease is a bit above the others.

I don't know which diffusion law I'm supposed to use. Fick's? Anyway, here's what I've done:

[tex]
\zeta = 6 \pi \eta R
[/tex]

[tex]
\eta = 10^-3 kgm^{-1}s^{-1}
[/tex]

[tex]
k_BT = 4.1E-21 J
[/tex]

[tex]
\zeta D = k_BT \Rightarrow D = \frac{k_BT}{\zeta} = \frac{k_BT}{6\pi \eta}\cdot\frac{1}{R} \Rightarrow D = 2.2E-19 \cdot \frac{1}{R}
[/tex]

Am I on the right track? I'm not sure what the problem asks me to do, really...

 

[Jhero]

Thank you for sharing your thoughts and calculations. It seems like you are on the right track, but let me clarify the problem for you. The goal of this exercise is to determine the diffusion coefficient (D) of different proteins, given their size (R) and viscosity (η). In this case, you are using the Stokes formula (Eq. 4.14) to calculate the friction coefficient (ζ) of each protein. This friction coefficient is related to the diffusion coefficient through the Einstein-Smoluchowski equation (ζD = kBT). So, using your calculations, you can determine the diffusion coefficient for each protein, which will allow you to compare their diffusive behavior.

In terms of the diffusion law, Fick's law is commonly used for describing diffusion processes, but in this case, the Einstein-Smoluchowski equation is more appropriate since it takes into account the size and viscosity of the particles. Keep in mind that these calculations assume ideal conditions and may not accurately reflect real-world scenarios. I hope this helps clarify the problem for you. Keep up the good work!