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## Main Question or Discussion Point

An allowed state of a molecule in a gas that is in a box of length L can be represented by a point in 3 dimensional K-space, and these points are uniformly distributed.In each direction points are separated by a distance π/L. A single point in K-space occupies a volume (π/L)^3.

The number of allowed states with wave vector whose magnitude lies between k and k+dk is described by the function g(k)dk, where g(k) is the density of states.This number is then given by:

g(k)dk= (volume of k-space of one octant of a spherical shell)/ (volume in k-space occupied per allowed state)

Then [itex]g(k)dk=\frac{1/8\times 4πk^{2}dk} {2π^2}[/itex]

My question is : Can we say that dk=(π/L)^3 ?

The number of allowed states with wave vector whose magnitude lies between k and k+dk is described by the function g(k)dk, where g(k) is the density of states.This number is then given by:

g(k)dk= (volume of k-space of one octant of a spherical shell)/ (volume in k-space occupied per allowed state)

Then [itex]g(k)dk=\frac{1/8\times 4πk^{2}dk} {2π^2}[/itex]

My question is : Can we say that dk=(π/L)^3 ?