How Do You Calculate the Multiplicity of a Two-Dimensional Ideal Monatomic Gas?

[jlmac2001]

Consider an ideal monatomic gas that lives in a two-dimensional universe ("flatland"), occupying an area A instead of a volume V. Find a formula for the multiplicity of this gas.


I arrived at this formula. Is it correct?:

1/N!(A^N/h3N)(pi^3N/2/3N/2)!(sqrt(2mU))^3N

 

[solar nebula]

its wrong:

it should be
[(1/N!)*((A*pi)^N)*(2MU)^N]/ (h^2N)*(N!)