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**Boltzmann statistics -- finding the number of particles**

## Homework Statement

A column of water contains fine spherical metal particles of radius 2 x10

^{-8}m, which are in thermal equilibrium at 25C. If there are 1000 particles per unit volume at a given height, how many particles would be found in the same volum 1 mm higher? The density of the metal is 2 x10

^{4}kg m

^{-3}. Hint: use gravitational force and buoyancy in water and compute change in potential energy

## Homework Equations

F

_{net}= [tex]\rho[/tex]Vg - mg ([tex]\rho[/tex] is density, V is volume, g is gravity, m is mass)

F*d = -mg [tex]\Delta[/tex]h (h is height, d = height, F = F

_{net}

n(E) = g(E)f

_{b}(E) = A g(E)e

^{-E/kT}

n(E) = number of particles with energy E

g(E) = statistical weight of the state with energy E

A = normalization constant whose value depends of the system

k = boltzmann constant

T = temperature

E = energy

## The Attempt at a Solution

What I did was just substitute F

_{net}= [tex]\rho[/tex]Vg - mg

into F*d = -mg [tex]\Delta[/tex]h which gives me the change in potential energy. I'm not sure what to do with the boltmann distribution formula after that or do I even need it? I'm just stuck and don't know where to go. Any help will be appreciated

Thank you