Problem

Electrophoresis. Electrophoresis is a process used by biologists to separate different bi...

Electrophoresis. Electrophoresis is a process used by biologists to separate different biological molecules (such as proteins) from each other according to their ratio of charge to size. The materials to be separated are in a viscous solution that produces a drag force FD proportional to the size and speed of the molecule. We can express this relationship as FD = KRυ, where R is the radius of the molecule (modeled as being spherical), υ is its speed, and K is a constant that depends on the viscosity of the solution. The solution is placed in an external electric field E so that the electric force on a particle of charge q is F = qE. (a) Show the electric field is adjusted so that the two forces (electric and viscous drag) just balance, the ratio of q to R is Kυ/E. (b). Show that if we leave the electric field on fir a time T, the distance x that the molecule moves during that time is x = (ET/k)(q/R). (c) Suppose you have a sample containing three different biological Molecules for which the molecular ratio q/R for material 2 is twice that of material 1 and the ratio for material 3 is three times that of material 1. Show that the distances migrated by these molecules after the same amount of time are x2 = 2x1 and x3 = 3x1 in other words material 2 travels twice as far as material 1, and material 3 travels three times as, far as material 1. Therefore we have separated these molecules according to their ratio of charge to size. In practice, this process can be carried out in a special gel or paper, along which the. biological molecules migrate. (Fig.). The process can be rather slow, requiring several hours for separations of just a centimeter or so.