Hi, I'm doing a course in bionanophysics and am really struggling with some of the calculations, can anyone help?

Consider particles of radius r and mass m randomly distributed in a column of water. What will the distribution of particles be if they are allowed to settle for a long time?

i)Obtain an expression for the change in potential energy, \Delta U if a particle moves a distance \Delta z.

ii) From consideration of thermal energy kT and answer from i) give an expression for the distribution of the particles as a function of height, z.

iii) If the height, h=4cm and the object is a protein myoglobin, molar mass=17000g/mole calculate the distribution at the top of the tube as a fraction of the concentration at the bottom - i.e. c(h)/c(0). Assume net mass=0.25m

iv) If h=25cm and the objects are fat droplets (density 0.91g/cm^3) find c(h)/c(0) in equilibrium.