A colloidal suspension contains particles of mass m and density ⇢c suspended in water of density ⇢w in a gravitational field of strength g. (a) Show that the number density n(z) = n0 exp [m(⇢c⇢w)gz ⇢ckBT ] where n0 is the density at the bottom of the vial and z is vertical distance measured from the bottom of the vial. (b) By balancing the di↵usive flux (from the concentration gradient) with the sedimentation flux (from gravity), derive the Stokes-Einstein equation D = kBT/(6⇡⌘a) (Hint: Consider both the di↵usive flux, J1 = Ddn/dz, and the sedimentation flux, J2 = vtn, and balance J1 and J2 across a thin slice of thickness dz).

Time remainin52: 42the chart shows data for a moving object.which conclusion is best supported by the information inthe chart? time (s)velocity (m/s

This is really important 1.which of the following prefixes represents the largest value? (2 points)gigahectorkilomilli2.which of the following types of graphs is best for plotting the mean, median, and mode of data? (2 points)bar graphbox-and-whiskercircle graphstem-and-leaf

Two loudspeakers, 5.5 m apart and facing each other, play identical sounds of the same frequency. you stand halfway between them, where there is a maximum of sound intensity. moving from this point toward one of the speakers, you encounter a minimum of sound intensity when you have moved 0.33 m . assume the speed of sound is 340 m/s.part a) what is the frequency of the sound? part b) if the frequency is then increased while you remain 0.21 m from the center, what is the first frequency for which that location will be a maximum of sound intensity? express your answer to two significant figures and include the appropriate units.