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Given the Maxwell-Boltzmann distribution:

f(v) = 4*pi*[m/(2*pi*k*T)]^(3/2)*v^2*exp[(-m*v^2)/(2*k*T)]

Observe the appearance of the Boltzmann factor exp[(-m*v^2)/(2*k*T)] with E = 1/2(mv^2)

Assuming a fixed temperature and mass, one can simplify this equation:

f(v) = a*v^2*exp[-bv^2]

a = 4*pi*[m/(2*pi*k*T)]^(3/2)

b = m/(2*k*T)

In order to calculate the fraction of particles between two speeds v1 and v2, one should evaluate the definite integral:

∫f(v)dv

Here is an link to integral-tables, http://integral-table.com/

How would I solve this problem for let's say a certain amount of moles with hydrogen between two different velocities? Best regards, Tor