Question

How do you get to the answer?

Suppose a given protein with a diffusion coefficient 2.5 ×10−10m2/s is at the center of a tube at time zero. How far do you expect to find it after 2 ms? You can estimate your answer using the root-mean-square displacement of the protein.

Answer 1

Diffusion is the movement of the molecules from its region of higher concentration towards a lower concentration. It is important to estimate the time taken or distance travelled by the molecules through diffusion.

It can be estimated using the formula:

t = X2/ 2D

where D is the diffusion coefficient of a solute

  x is the mean distance traveled

  t is the elapsed time since diffusion began

From the problem, we know that

D = 2.5 x 10-10 m2/s or 2.5x 10-6 cm2/s

t = 2 Millisecond or 2x 10-3 s

Therefore, we can find x which is the root mean square displacement of the protein.

X2 = t x 2D

= 2 x 2 x 10-3 x 2.5 x 10-6 cm2/s

= 10-8 cm2/s

Therefore X = 10-8

Answer : X = 10-4 cm.