Excitation Equation and Velocity Distribution

If we take the derivative of the expression in Eq. (10.33) with respect to T, we obtain 

The density of points along any one of the diameters of the point cloud (e.g., along the axis) is reflected in the bell curve in Fig. 10.6b. 

In order to derive the particle velocity distribution of a gas we need a trick. We imagine all the particles with the same velocity v to be molecules of a substance B(o) and the entire gas as a mixture of a large number of such substances. However, we run into a difficulty at this point. The number of particles having 

Assumptions To continue our derivation, we need the mass action equation valid for dilute gases 

We also need another important equation. When the molecules of a substance are excited and lifted to an energy state higher by w without otherwise changing them or their milieu (temperature, pressure, cmicentration, type of solvent, field strength, etc.), the potential of the substance will increase by the molar energy w/r  

---