Interpreting Luminescence Data (Worksheet)
- Page ID
- 67405
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Consider \(\bar {\nu} = R_H \left ( \frac {1}{f^2} - \frac {1}{i^2} \right)\) (Equation 2.8) and use the luminescence data in the following table to construct a graph showing the linear relationship between the wave number values for the transitions and the Rydberg index i. File links to the data are provided with the table. Construct your graph so each Rydberg series appears as a separate line. A Rydberg series consists of all the transitions that have the same value for the index f. A Mathcad worksheet with helpful information that will help you is provided.
- Examine your graph. Why are the lines parallel or not parallel to each other? Why are they displaced from each other? What is the significance of the y-intercept, the x-intercept, and the slope?
- Evaluate the Rydberg constant from your graph. Compare this experimental value to the one you obtained in Exercise 2. and to the literature or textbook value (109,677.581 cm-1). What insight do you gain from these comparisons?
- Predict the wave number values in the Rydberg series for the three transitions that have the smallest values of i with f = 7. In which spectral region do these lines lie?
- Different series of spectral lines have the names of the different people who discovered them. Why didn’t one person discover all the series?
- What happens to the spacing between the lines as i gets larger and approaches infinity? Why does this change occur?
- The transition wave number values approach a limit as i approaches infinity. What is this limiting value for each of the series?
- Can you determine the energy it takes to ionize a hydrogen atom from the luminescence data? If so, compare your value with the literature or textbook value (13.5983 eV). Propose a testable reason for any discrepancy.
- Use the luminescence data to construct an energy level diagram, drawn to scale, for the hydrogen atom. Label each energy level with an integer corresponding to a Rydberg index. Show how the transition wave number values are related to the energies of these levels. Identify the ionization energy in your diagram as well.
Hydrogen Atom Luminescence Data
The data in this Table were obtained from American Institute of Physics Handbook (McGraw-Hill, New York, 1957) pp. 7-210 and 7-211. The lines in this table with Series names are those first identified by the person after whom the series is named.
Text and Excel Files containing the H atom luminescence data.
Hydrogen Atom Data Text file: HAtomDataTab.txt
Hydrogen Atom Data Excel file: HAtomDataXL.xls
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