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. Write an equation for a Gaussian. Give3 examples of measurements you expect a Gaussian distribution and 3 for non Gaussian. Estimate the speed of any particular gas molecule travelling in air at room temperature.

Solution

The avaerage kinetic energy of each molecule is =>KE(avg)=3/2*k*T

where k=Boltzmann\'s constant=1.38*x 10^-23 joules/kelvin

T=temperature in kelvin=301k(room temperature)

KE(avg)=>3/2*(1.38x10^-23)*(301)=6.23x10^-21 joules

KE=1/2*m*v^2

where m=mass, v->velocity

=>v=(2KE/m-> A

m=>4.65 x10^-26 kg

put this in A

v=2(6.23x10^-23 J)/4.65x10^-26kg = 518 m/s(This is the speed)