## 3 Results and Discussion
### Spectroscopic Characterization
#### 3.3.4 Electron Density
The Doppler broadening, that it is produced by the movement of emitting particles in respect to the observer, and the instrumental one, given by the resolution of the optical system, \(\Delta\lambda_{I}=0.108\) nm in this set-up. The Doppler broadening depends on the gas temperature by the following expression [30, 31, 32]:  
\[\Delta\lambda_{D}(\mathrm{nm})=7.2\times 10^{-7}\sqrt{\frac{T_{g}}{M}}\lambda \tag{16}\]  
where \(\lambda\) is the wavelength of line and \(M\) is the atomic mass, 656.3 nm and 1 g/mol for H\({}_{\alpha}\), respectively. The combination of both of these Gaussian broadenings is a Gaussian profile with a FWHM [33, 34, 35, 36, 37]:  
\[\Delta\lambda_{G}=\sqrt{\Delta\lambda_{D}^{2}+\Delta\lambda_{I}^{2}} \tag{17}\]  
It must be noted that, the superposition of the Gaussian (Doppler + Instrumental broadenings) and Lorentzian (Stark + van der Waals broadening) profiles will result in the Voigt profile (see Figure 14). Using the Origin software, the fitting procedure was performed and the FWHM of the Lorentz broadening was distinguished. Removing the \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Species** & **Reduced Mass, \(\mu\)** & **Polarizability, \(\alpha\)** & **Volume Fraction, \(X\)** \\ \hline
**C\({}_{4}\)H\({}_{10}\)** & 0.98305 & \(8.10\times 10^{-24}\) cm\({}^{3}\) & 0.65 \\ \hline
**C\({}_{3}\)H\({}_{8}\)** & 0.97778 & \(6.3\times 10^{-24}\) cm\({}^{3}\) & 0.35 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Parameters of C\({}_{4}\)H\({}_{10}\) and C\({}_{3}\)H\({}_{8}\) for the calculations of van der Waals broadenings. van der Waals effect of this total Lorentz FWHM from Equation (15), the Stark broadening and, consequently, the plasma electron density could be calculated. Figure 14 shows an example of this fitting for the case of an applied AC voltage kept at 14 kV with the C\({}_{4}\)H\({}_{10}\)/C\({}_{3}\)H\({}_{8}\) gas mixture, an electrode rotation frequency of 18,000 rpm and a 1 sLm gas flow rate. The FWHMs of the Gaussian and Lorentzian profiles are equal to \(\Delta\lambda_{G}\) = 0.105 nm and \(\Delta\lambda_{L}\) = 0.093 nm, respectively. Figure 15a shows the changes of the electron number density as a function of applied voltages. It is obvious that by increasing the applied voltage, the electron number density is raised. This is owing to the fact that, the electric field between the electrodes is strengthened by raising the voltage. On the other hand, the charged species is more accelerated in the electric field and the ionization collision will be higher. Hence, the electron density is increased. The electron number density is also grown by raising the rotation frequency of the power electrode at the maximum applied voltage as shown in Figure 15b. This growing of electron density is due to a secondary effect produced by hydrogen (see Equation (6)). As mentioned, the density of hydrogen atoms rises with the electrode rotation frequency. These hydrogen atoms produce more ionization and consequently a higher electron density. At the higher gas flow rates, the influences of ionizing collisions on the neutral particles will significantly decrease, as shown in Figure 15c. The results of the electron density agree with the H\({}_{2}\) formation detected by the GC. The hydrogen selectivities (see Figure 6) had similar behaviors to the obtained ones for the electron density. This confirms that the mechanisms that lead to the hydrogen formation were governed by electron kinetic energy. Figure 14: Comparison of the Voigt, Lorentzian, and Gaussian broadenings by fitting on experimental data.