User:Emran M. Qassem/Notebook/Physics 307L/2010/11/15

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Balmer Series

Purpose

  • To determine the Rydberg constant by measuring the wavelengths of the spectrum of Hydrogen and Deuterium in the Balmer series.
  • This can be done using Balmers equation and relating the wavelengths to the principle quantum number of the initial state.

Equipment

Spectrometer
Crystal
Wavelength Positioner
Bulb
Deuterium Spectrum
  • Constant Deviation Spectrometer
  • Spectrum Tube Power Supply Model SP200, 5000 volts, 10MA.
  • Mercury, Hydrogen and Deuterium tubes

Safety

  • High voltage on power supply, possibility of shock.
  • Sensitive crystal, do not drop or over tighten clamp.
  • Bulbs are fragile, be careful not to drop.
  • Bulbs get hot, be careful when handling so as not to burn yourself.
  • Spectrometer is very old and precise equipment, do not force or jam things.

Setup

From Professor Gold's Manual:

  • Before turning out the lights or mounting the bulb, focus the cross-hairs by pulling the eyepiece in and out.
  • Mount the mercury bulb and turn it on, being careful not to shock yourself.
  • Open the slit width to a wide opening and place the bulb close to the slit, approximately 1 cm or less away.
  • Change the wavelength positioner (rotates the crystal) until you can see a spectrum line.
  • Look through the eyepiece and turn the knurled nob to focus the slit.
  • Adjust the slit width so that it appears to be a thin line with enough intensity to see it well.

Procedure

  • Calibration
    • Based on the color you see, use the table of wavelengths to find out what wavelength you are looking at.
    • Set the wavelength positioner to that wavelength.
    • Turn the crystal manually so that the line appears in the cross-hairs and coincides with the wavelength positioner value.
    • Find each spectrum line and write down the actual value and the measured value and record the difference so that you have a calibration.
  • Actual experiment
    • Now mount Hydrogen and Deuterium and measure all of their spectral lines and record their wavelengths.
    • Look up the principle quantum numbers for Hydrogen (balmer series image works).
    • Use this data with the Balmer equation to calculate R.


Data

Balmer Series XL Doc

Calculations

We decided to calculate 2 separate Rydberg constants for Hydrogen and Deuterium. From the following equation:

[math]\displaystyle{ 1/wavelength=R*(1/2-1/n^2)\! }[/math]

solving for R:

[math]\displaystyle{ R=\frac{1/wavelength}{1/2-1/n^2}\! }[/math]

Plotting this and using least squares method, we found R for each:

[math]\displaystyle{ R_H=1.10(4)*10^7/m\! }[/math]
[math]\displaystyle{ R_D=1.104(5)*10^7/m\! }[/math]

Error

With the Rydberg constant for Hydrogen accepted value at:

[math]\displaystyle{ R = 1.0974*10^7/m\! }[/math]

and our measured values ranging from:

[math]\displaystyle{ 1.06*10^7 \lt R \lt 1.14*10^7/m\! }[/math]

We can see the results are within 1 sigma away from the accepted value.

For Deuterium, the results are even better, and our error bars are almost not visible as our data is almost directly on the best fit line found by the least squares method.

When we did our mercury calibration, we found that our measured wavelength was -9 off from the actual wavelength for 690. This was throwing our results off so we decided to check what would happen if we changed it to 2, more close to the rest of our calibration differences. This made our results a lot better. My lab partner insisted we made a mistake in our measurements, so we decided to keep it at a calibration of 2 and keep the better results and match the trend of error correction.

Acknowledgments/citations

Randy for calculations.


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