## 3 Results
### Electron Plasma Number Density  
To estimate the electron-number-density, the hydrogen line-profile was used and a well-isolated Stark broadened line profile of carbon belongs to the emission spectrum of the _P. harmala_ seed sample-(\(\alpha\)). The estimated number density using the full-width-at-half-area (FWHA) of a hydrogen (H\({}_{\alpha}\)) spectral-line emits at 656.3 nm wavelength is depicted in Figure 4a. The measured line profile data (blue color) and black dotted lines (vertical) indicate the FWHA produces as (0.643 \(\pm\) 0.5) nm. A simple relation for measurement of electron-density using H\({}_{\alpha}\)-line is taken from [PERSON] et al. [48] and [PERSON] et al. [49]. \[\omega_{FWHA}=5.49\text{\AA}\times(\frac{N_{e}}{10^{17}\text{cm}^{-3}})^{0.67965} \tag{2}\]  
Here, \(\omega_{FWHA}\) represents the full-width-at-half-area and \(N_{e}\) denotes the number density. The \(\omega_{FWHA}\) parameter is computed through the relation, \(\omega_{FWHA}=\delta\omega_{2}-\delta\omega_{1}\). The plasma density calculated using Equation (2) is \((1.26\pm 0.5)\times 10^{17}\) cm\({}^{-3}\). The full-width-at-half-maxima, \(\Delta\lambda_{1/2}\) (FWHM) of C spectral-line was estimated using Voigt-fitting-line-profile by considering the 0.06 \(\pm\) 0.01 nm instrumental-width, the Stark-width (\(\omega_{s}\)) and 0.005 nm the  
Figure 4: (a) H\({}_{\alpha}\) spectral line; (b) Stark-broadened-line-profile of C-I spectral line emits at wavelength 247.86 nm. Figure 3: [PERSON]–[PERSON] plots using the well-isolated Ca (I) and Ca (II) spectral lines. Doppler-width. The Stark-width relation versus FWHM and plasma-electron-density is shown as follows [49]:  
\[N_{e}\left(cm^{-3}\right)=\frac{\Delta\lambda_{\frac{1}{2}}(FWHM)}{2\omega_{s}( \lambda,T_{exc})}\times 10^{16} \tag{3}\]  
Here, \(\omega_{s}\) represents the parameter of Stark-broadened, \(N_{e}\) shows the plasma-electron-density and \(T_{exc}\) shows the excitation-temperature. The Stark-broadened-line-profile of the C I emission line at 247.86 nm due to 2p3s \({}^{1}\)P\({}_{1}\)\(\rightarrow\) 2p\({}^{2}\)\({}^{1}\)S\({}_{0}\) transition is shown in Figure 4b. The experimentally measured data-points (blue-circles) and Voigt fitting profile (the solid-orange-line) gives the FWHM (0.743 \(\pm\) 0.5) nm. The Stark-broadened-parameter (the 0.0361 nm taken from literature [50]), the electron plasma density \(N_{e}\) is approximated as \((1.03\pm 0.5)\times 10^{17}\) cm\({}^{-3}\). An excellent agreement can be found among densities calculated using Stark-Broadened spectral-line-profile of C I at corresponding wavelength 247.8 nm and the hydrogen-H\({}_{\alpha}\) emits at wavelength 656.3 nm. Besides, an average calculated number-densities \((1.15\pm 0.5)\times 10^{17}\) cm\({}^{-3}\) was used to estimate the quantification of _P. harmala_ samples with CF-LIBS. The estimated uncertainty in the electron number densities appears due to the uncertainties in the FWHM from the fitting procedure, from the instrumental-width, and star-broadened parameter. A criterion proposed by [PERSON]--\(N_{e}\left(\text{cm}^{-3}\right)\geq 1.6\times 10^{12}\sqrt{\left(T_{exc} \right)}\left(\Delta E_{(eV)}\right)^{3}\)[51] --is necessary to satisfy LTE conditions in plasma, where \(T_{exc}\) is the excitation-temperature in kelvin (K) and \(\Delta\)E represents the transition energy in electron volt (eV). The calculated \(N_{e}\) value was \(\sim 1\times 10^{15}\) cm\({}^{-3}\), which is less than the \(N_{e}\) value estimated from relations (2) and (3). This shows that the plasma satisfies the condition of LTE. The plasma condition of LTE has also been established by measuring the diffusion-length criterion for an inhomogeneous-plasma [52]. As per following condition, the characteristic variation length \"\(d\)\" is much larger than the diffusion-length \((10\lambda<d)\). In this work, the diffusion length has been calculated by using the neutral carbon emission line (C I). The diffusion length was calculated to be \(\lambda\sim 1.7\times 10^{-2}\) mm.