A motile bacteria uses its flagella to swim at 30 mu msec bu

A motile bacteria uses its flagella to swim at 30 mu m/sec but every 1 sec it \"tumbles\" and changes its direction to a new randomly chosen direction in 3D. What is its apparent \"diffusion\" constant because of this motion. For a 50 nm vesicle plot how would Mean square displacement evolve with time (with real numbers on the plot) it it were to diffuse freely On this plot, also plot the MSD if it were keep to be transported by a molecular motor at 1 mu m/sec. Plot such that you show where do the two MSDs cross? Write what the plot tells you about dependence of preferred mode of transport on target distances. Estimate the size of a water molecule starting from its density with short precise explanations.

Solution

We can estimate the size of water molecule by following way:

Using Avogadro’s concept 1 mol = 6.02 x 10²³ molecules

1 mol of water = 18 g and 1 g= 1cm³

So we have the volume of 1 mol water which is 18cm³, this volume is for 6.02 x 10²³ molecules

Now the volume for 1 molecule = total volume/ total number of mole

18 / 6.02 x 10²³ 18/ 6 x 10²³ = 3 x 10^-23 cm³

Now take cubic root of the volume = [3 x 10^-23 cm³ ]^1/3 1.44 x 10^-8 cm {approximate}

This is in centimeter which takes as size of molecule. Or, 1.44 x 10^-10 m = 1.44 Angstrom.

The density is = weight/ volume = 18g/18 cm³ = 1g/cm³ which is for 6.02 x 10²³ molecules

For 1 moleucle = 1/ 6.02 x 10²³ =0.17 x10^-23 g/cm³