1) [Brownian Motion and Transport Motion]

In a living cell, a ball-shaped organelle of radius r = 500 nm and mass of

16.6x10-22 kg undergoes Brownian motion before it encounters a motor

protein. Once the organelle is bound to the motor protein, the organelle is

transported with a speed v=1.00 μm/s by the motor protein along a linear track.

The solution environment of the cell has temperature T=37°C and viscosity

¹-10-³ Ns/m². Suppose you do a one-dimensional measurement of the

organelle's position to distinguish the two types of motion.

a) Calculate the relaxation time for the organelle.

b) Suppose you have an optical microscope that uses blue light. Are you sure

that the instrument is able to image the organelle? Give a reason for your

answer.

c) In case of Brownian motion, what is the root-mean-square speed of the

organelle you would expect from your measurement?

d) In case of Brownian motion, what is the root-mean-square displacement of

the organelle you would expect from your measurement for a period of t =

5.00 s?

e) For the transport by a motor protein, what is the root-mean-square

displacement of the organelle you would expect from your measurement

for the same period of t = 5.00 s?