## 3 Results and Discussion
### Spectroscopic Characterization
#### 3.3.4 Electron Density  
To understand the dissociation of molecules by electron impact in the formed plasma discharge media, the electron number density in the developed plasma reactor must be calculated. The Stark broadening analysis of the hydrogen Balmer series emission lines is one of the most usual spectroscopic methods to obtain the electron density of the plasma discharge [27, 28, 29]. In this work, the Stark broadening of the \(\alpha\)-series (H\({}_{\alpha}\)) at the wavelength of 656.3 nm was used. Several mechanisms separate the emission line of its monochromatic behavior and produce a broadening in this line. The interaction of emitting particles with the charged particles produces a Stark broadening that depends on the density of these particles, i.e., electron density, by the following expression [30]:  
\[\Delta\lambda_{stark}(\mathrm{nm})=1.097\left(10^{-17}n_{e}\right)^{1/1.47135} \tag{12}\]  
with the electron density \(n_{e}\) in cm\({}^{-3}\). If we can determine the value of this broadening, the Equation (12) can be used for the calculation of electron density. The other broadening  
Figure 13: Changes of the electron temperature with different (**a**) applied voltages on the stationary power electrode and 1 sLm gas flow rate (3% error), (**b**) rotational frequencies of power electrode at 14 kV applied voltage and 1 sLm gas flow rate (2% error), and (**c**) gas flow rates at 14 kV applied voltage and 18,000 rpm rotation frequency of the power electrode (2% error). mechanisms of the full width half maximum (FWHM) of the line must be identified and eliminated for this determination. The pressure broadening occurs when the states of the emitters are disturbed by the neutral species collisions. There are two types of this broadening: resonant broadening, due to the dipole-dipole interactions of the emitter with the ground-state atoms of the same element, and van der Waals broadening, that is produced by collisions with other species. For the hydrogen lines in this discharge, the resonant broadening is neglected by the small concentration of the hydrogen atom. Van der Waals broadening can be estimated by [30,31]:  
\[\Delta\lambda_{vdW}(\mathrm{nm})=8.18\cdot 10^{-26}\ \lambda^{2}\left(\alpha \left\langle R^{2}\right\rangle\right)^{2/5}\left(\frac{T_{g}}{\mu}\right)^{3 /10}\frac{P}{kT_{g}} \tag{13}\]  
where \(\mu\) is the reduced mass of the colliding particles, \(\lambda\) is the wavelength of the line (656.3 nm in our case), \(\alpha\) is the polarizability of the perturber species, \(\left\langle R^{2}\right\rangle\) is the difference of the square radius of the upper and lower levels of emitting particles, \(T_{g}\) is the gas temperature, and \(P\) is the pressure (1 atm). In the discharge of this work, the main perturbers were the C\({}_{4}\)H\({}_{10}\) and C\({}_{3}\)H\({}_{8}\) gases that compounded the LPG gas. The van der Waals of the gas mixture can be calculated by:  
\[\Delta\lambda_{vdW}(\mathrm{nm})=X_{\mathrm{C_{4}H_{10}}}\Delta\lambda_{vdW}^ {\mathrm{C_{4}H_{10}}}+X_{\mathrm{C_{3}H_{8}}}\Delta\lambda_{vdW}^{\mathrm{C _{3}H_{8}}} \tag{14}\]  
where \(\Delta\lambda_{vdW}^{\mathrm{C_{4}H_{10}}}\) and \(\Delta\lambda_{vdW}^{\mathrm{C_{3}H_{8}}}\) are the van der Waals broadenings of the butane and propane gases, respectively, and \(X_{\mathrm{C_{4}H_{10}}}\) and \(X_{\mathrm{C_{3}H_{8}}}\) are the volume fractions of these gases. The parameters that are needed to calculate the van der Waals broadening of the C\({}_{4}\)H\({}_{10}\) and C\({}_{3}\)H\({}_{8}\) gases are given in Table 5. For these calculations, the gas temperature of the Section 3.3.2 was considered. Both these mechanisms contribute with a Lorentzian profile whose FWHM is given by [29]:  
\[\Delta\lambda_{Lorentz}(\mathrm{nm})=\Delta\lambda_{Stark}+\Delta\lambda_{vdW} \tag{15}\]  
In addition to these both Lorentzian effects, there are other mechanisms that produce a Gaussian profile.