The kinetic energies Maxwellian distribution of molecules

We will now find the distribution function of the values of molecule kinetic energies. For this purpose we shall express the relative number of those molecules having speeds in interval n-n+tio using the kinetic energies expression s corresponding to these speeds. Express the equal number of molecules on velocities and energies 

Make a substitution of variables in expression (3.3.6). As muV2=e then, = 2dm and i) = V2/mVg. Taking into account eq. (3.3.8.), expression (3.3.6) will then be as follows  

The distribntion obtained allows us to estimate the concentration of chemically active molecnles, which can overcome the activation barrier Q and get in touch with another molecule to produce a new prodnct. To find the relative concentration of molecnles with kinetic energy g 2, we shonld calculate an integral 

There are no such integrals in the mathematical tables. We can see that at large g, the main contribution to the result is made by the exponent the multiplier Vg contributes vaguely in comparison with the exponent and can be neglected. Therefore, the situation is simplified and calculation of the integral results in 

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