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after that the relative intensity becomes chaotic and does not ap- pear to follow any pattern. 3. Calculating the spectra of Lithium

Figure 3 after that the relative intensity becomes chaotic and does not ap- pear to follow any pattern. 3. Calculating the spectra of Lithium

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In this graph, the Lyman series shows all the transitions that start with nl = 1. The first datapoint on the left shows the transition from nl = 1 to n2 = 2. It goes to n2 = 10. It can be seen that this corresponds to the shortest wavelength, highest energy transi- tions. We then see the Balmer series starting at nl =2. Despite the obvious pattern seen in the data, there are no references to any- We have seen that the Rydberg formula can be used to calculate the atomic spectra of Hydrogen. What we need to do is to find a “pattern” to the data. If we just group the spectral data so that we group all the lines that belong to the same n1 together, the graph reveals a very interesting staircase pattern.
In this graph, the Lyman series shows all the transitions that start with nl = 1. The first datapoint on the left shows the transition from nl = 1 to n2 = 2. It goes to n2 = 10. It can be seen that this corresponds to the shortest wavelength, highest energy transi- tions. We then see the Balmer series starting at nl =2. Despite the obvious pattern seen in the data, there are no references to any- We have seen that the Rydberg formula can be used to calculate the atomic spectra of Hydrogen. What we need to do is to find a “pattern” to the data. If we just group the spectral data so that we group all the lines that belong to the same n1 together, the graph reveals a very interesting staircase pattern.
The following is the calculated He I spectral data based on these formulas. Columns N1 & N2 represent the electron shell transi- tion number. The third column represents the observed wave- length and fourth represents the calculated wavelength. The last column shows the difference between the observed and calculat- ed values which is typically less than a percent difference. If you were to plot the calculated values over the experimental values, you could hardly tell the difference.
The following is the calculated He I spectral data based on these formulas. Columns N1 & N2 represent the electron shell transi- tion number. The third column represents the observed wave- length and fourth represents the calculated wavelength. The last column shows the difference between the observed and calculat- ed values which is typically less than a percent difference. If you were to plot the calculated values over the experimental values, you could hardly tell the difference.
The Excel spreadsheet used to create this graph and a Microsoft word document of this article is available upon request (spectra- HE.xls). Using the data from the NIST database the spectral lines for He I] and He I can be graphed. Remember that the He II lines are com- pletely predicted by the extended Rydberg formula. But we can clearly see that the He I spectra also appears as this same stair- case pattern, but at a longer wavelength. This nearly identical shape suggests that the He I spectra can be calculated as simply being a scaled version of the He II spectra.
The Excel spreadsheet used to create this graph and a Microsoft word document of this article is available upon request (spectra- HE.xls). Using the data from the NIST database the spectral lines for He I] and He I can be graphed. Remember that the He II lines are com- pletely predicted by the extended Rydberg formula. But we can clearly see that the He I spectra also appears as this same stair- case pattern, but at a longer wavelength. This nearly identical shape suggests that the He I spectra can be calculated as simply being a scaled version of the He II spectra.
This is just a simple plot of the line data found in the NIST data- base ordered by species and grouped by transitions. What may have appeared to be a random scatter chart of lines, now appears as a very ordered set of data. The same spectra analysis can be applied to the next element in the periodic table which is lithium. The graph of the lithium looks like this:
This is just a simple plot of the line data found in the NIST data- base ordered by species and grouped by transitions. What may have appeared to be a random scatter chart of lines, now appears as a very ordered set of data. The same spectra analysis can be applied to the next element in the periodic table which is lithium. The graph of the lithium looks like this:
The relative intensity can be calculated for N1=1,2,3 as:
The relative intensity can be calculated for N1=1,2,3 as:
The analysis for the next element Beryllium becomes even more difficult as we are faced with a nearly continuous spectra. For example, to do the analysis of Be I, the only points that appeared to be known with any confidence are the very highest transitions which have very few spectral lines in the longest wavelengths. Based on the slope of those data points, the rest of the points were selected. For Be, even the ion identification needed to be occasionally ignored to find best fit data points. Due to this diffi- culty, the exact quality of the data point selection is questionable. However, there is enough data to speculate that the overall shape and slope of the graph is correct and the graph contains most of the brightest observed lines. Compared with lithium, we see that the Li III and Li II are closely spaced like Be IV and Be III. The next ion Li I and Be II appear to be further spaced away. Be I appears closely spaced with Be II. This similar pattern suggests that the ions may follow a predicta-
The analysis for the next element Beryllium becomes even more difficult as we are faced with a nearly continuous spectra. For example, to do the analysis of Be I, the only points that appeared to be known with any confidence are the very highest transitions which have very few spectral lines in the longest wavelengths. Based on the slope of those data points, the rest of the points were selected. For Be, even the ion identification needed to be occasionally ignored to find best fit data points. Due to this diffi- culty, the exact quality of the data point selection is questionable. However, there is enough data to speculate that the overall shape and slope of the graph is correct and the graph contains most of the brightest observed lines. Compared with lithium, we see that the Li III and Li II are closely spaced like Be IV and Be III. The next ion Li I and Be II appear to be further spaced away. Be I appears closely spaced with Be II. This similar pattern suggests that the ions may follow a predicta-
Related topics:
Atomic, Molecular, And Optical PhysicsQuantum PhysicsFoundations of Quantum MechanicsQuantum MechanicsAtomic SpectroscopyNuclear and Atomic PhysicsSpectral Graph TheorySolution of Schrodinger Equation
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