Spectrum of the hydrogen atom

Measure a part of the hydrogen atom spectrum and distinguish it from the spectrum of deuterium.

Experimental procedure

Notes:

  • Pay close attention during the experiment to the number of points that assemble each measured peak. You should have at least 10 points per peak.
  • For every peak you observe, report its center wavelength and, in addition, its standard deviation (i.e., error estimation).

Calculate the Rydberg constant

  1. Run a crude scan and determine the position of lines in the Balmer series of the spectrum.
    • What is the interval of your scan (in nm)?
    • How many lines did you observe?
    • Identify and assign the spectrum.
    • Did you expect to find more lines?
    • If you expected to find more lines, what are the reasons that more are not present?
    • If you have anticipated all the spectral lines, what led you to the conclusion that those lines, and only those lines, would be observed?
  2. Choose one observable spectral line wavelength and use it to optimize the hydrogen lamp location with respect to the entrance slit.
    • What was the spectral line wavelength you chose and why?
    • o Make sure that your signal is not saturated once you have completed your optimization. Think about how you can achieve this. The parameters you can change are entrance and exit slit widths, lamp position, voltage applied to the photomultiplier and grating step. Which parameters should you change in order to have unsaturated signal and in addition have good spectral resolution.
  3. After optimization, scan the whole spectrum again. What is the resolution you are using?
  4. Scan limited regions near each of several Balmer lines at high resolution, using the hydrogen tube. Extract the relevant parameters for each peak (numerical fitting with Origin, Matlab, or educated estimation).
  5. Calculate the Rydberg constant.Use the following table:
    6. Level number λ[nm]
    ... ...

    Calculate the reciprocal linear dispersion of the monochromator

    1. Select an observable peak. What is the optimal wavelength for measurement?
    2. Measure the width of the line for different exit slit widths. Use the Origin software to find the width of the peak at half height.
      • How does the line width depend on slit width?
      • Calculate the reciprocal linear dispersion of the monochromator.
      • Compare your calculation for the reciprocal linear dispersion of the monochromator with the known manufacturer value.

    Estimate the number of dynodes

    1. Select the peak with the highest intensity and the peak with the lowest intensity.
    2. For each peak, find the dependence of signal intensity by changing the voltage applied to the photomultiplier.
      • What kind of dependence do you expect?
      • Estimate the number of dynodes.

    Deuterium/Hydrogen ratio

    For the Deuterium/Hydrogen ratio calculation section you must read the article written by Lutfur R. Khundkar titled "Mass Ratio of the Deuteron and Proton from the Balmer Spectrum of Hydrogen". Download here.

    1. Change the light bulb to deuterium.
    2. Scan limited regions near each of several Balmer lines at high resolution using the deuterium tube. This tube contains sufficient concentration of residual hydrogen to allow the H-atom lines to be used as internal standards.
    3. 3. Calculate the mass ratio of the deuteron to the proton using measured isotopic shifts in the Balmer series for each peak, and compare your results to that reported by Khundkar.
    4. Estimate the deuterium concentration in the lamp.

    Calibration:

    1. 1. Calibrate the line positions observed in the experiment using known lines of the mercury lamp, which you can find in the CRC handbook or in an online database such as NIST.
    2. Correct all your acquired data with the aid of this calibration curve.