Answer:
According to the law of atmospheres,
?..(1)
where
refer to
number density of particles at heights and respectively.
If
we consider the sedimentation equilibrium of suspended particles in a liquid,
then in place of mg, we will have to take effective weight of the suspended
particles.
Let
V = average volume of a suspended particle, = density of
suspended particle, =
density of liquid, m = mass of one suspended particle, m' = mass of equal
volume of liquid displaced.
According
to Archimede's principle, effective weight of one suspended particle
=
actual weight - weight of liquid displaced = mg - m' g
Also, Boltzmann constant,
where,
R is gas constant and is
Avogadro's number.
Putting,
mg in place of
mg and value of in
(i), we get
Which
is the required relation.
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