Density of molecules of gas as a of r is, n(r)=n0e−αr4
Total no. of molecules =∫0∞n(r)dv
∫0∞n0e−αr44πr2dr
To integrate this, substitute u=α3/4r3 this will give us dr=3α3/4r21du
Now, the integration will become, 3α3/44πn0∫0∞e−u4/3du
This shows that the numer of molecules is proportional to n0α−3/4