Maxwell Velocity Distribution

f[v_,m_,T_]:=4 π ((((m/(2 π k T))))^(3/2)) (v^2) (E^(-((m (v^2))/(2 k T))))

Is the function normalized?    100% probability of finding the particle between 0 to ∞   meters/sec.

Assuming[Re[(mass/(k Temp))]>0,(∫_0^∞)f[v,mass, Temp]\[DifferentialD]v]

Na=6.02 (10^23);
k = 1.38 (10^(-23));
Plot[{f[v,29 (10^(-3))/Na,293],f[v,29 (10^(-3))/Na,1000]},{v,0,2000}]

What fraction of the molecules are found between 330 m/s and 350 m/s?

Na=6.02 (10^23);
k = 1.38 (10^(-23));
(∫_330^350)f[v,29 (10^(-3))/Na, 293]\[DifferentialD]v

What is the most probable speed?

k = .;
m=.;
T=.;
Solve[(∂_v)f[v,m, T]==0,v]

What is the rms speed?     (Subscript[v, rms]^2) = ?

k =.;
m=.;
T=.;
Assuming[Re[(m/(k T))]>0,(∫_0^∞)(v^2) f[v,m,T]\[DifferentialD]v]

What is the average velocity?     (Subscript[v, av]) = ?

k = .;
m=.;
T=.;
Assuming[Re[(m/(k T))]>0,(∫_0^∞)v f[v,m,T]\[DifferentialD]v]