Physics307L F08:People/Smith/Notebook/2

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Contents

Experiment 2: Balmer Series

(Lab Partner F08:People/Martin Kyle Martin)

Purpose

In this experiment we will observe the Balmer Series of Hydrogen and Deuterium.

  • Review basic atomic physics.
  • Calibrate an optical spectrometer using the known mercury spectrum.
  • Study the Balmer Series in the hydrogen spectrum.
  • Determine the Rydberg constant for hydrogen.
  • Compare hydrogen with deuterium

Equipment

  • Constant deviation spectrometer. Mfd. by Adam Hilger, LTD, London England.
    • Refer to last year's lab manual for a diagram.
    • This spectrometer is slightly different than other spectrometers that I have previously used. This spectrometer has fixed arms and a rotating prism. It uses a Pellin-Broca constant-deviation prism to refract light, and a fixed telescope arm. It also has a rotating drum labeled with wavelengths; when this drum is rotated, the prism is rotates as well, shining different wavelengths of light on the objective scope. Previously, I have used spectroscopes which use a simpler, 60° prism and rotating telescope arm. In a constant deviation scope each ray of light passes through the prism in the angle of minimum deviation. This makes accurate measurement using a fixed arm spectroscope possible. For more information about the angle of minimum deviation, visit Georgia State's Hyperphysics site on it.
  • Spectrum tube power supply, Model SP2000. 5000 volts, 10mA. Mfd. by Electro-Technic Products, Chicago, Ill.
  • Various gas discharge tubes.
    • Mercury
    • Hydrogen
    • Deuterium
    • Na (Unable to find)

Equipment preparation

Position spectrometer in front of the gas discharge tube, open slit on spectrometer to a very narrow opening (maybe 0.5 mm or so). The larger the slit opening, the brighter the emission lines will appear, but the less sharp they will be. Focus objective scope. Try to calibrate spectrometer.

Calibration Procedure

Using a mercury gas discharge tube as light source (the wavelengths for the Balmer series of mercury are listed in lab manual), pick a color in the middle (green would probably be best). Turn the dial of the spectrometer until it displays the known wavelength of the emission line. Remove the prism cover, loosen clamp on prism and rotate the prism until the emission line is centered in the objective's cross hairs, tighten the clamp and replace the prism cover. The spectrometer is now calibrated.

Procedure for taking data

  • To take data, first put the desired gas tube in the spectrum tube power supply.
  • Turn on the power supply unit and wait a couple of minutes for it to warm up (the emission spectra should be uniform regardless of whether the unit is warm or not, but the brightness should increase as the unit warms.)
  • Starting at one end of the dial, turn the dial until you see a strong emission line. Note which way you've turned the dial, and record the wavelength the dial displays. Turn the dial in the same direction to move the emission line past the objective crosshair, so the line is just visible on the edge of the objective scope,
  • Turn the dial backwards to get a reading on the dial from the "other side". This is necessary because our spectrometer has a noticeable amount of "slop" or "backlash" - the gearing of the dial is slightly mushy, and will not give a precise reading.
  • Repeat this until all primary emission lines' wavelengths have been recorded.
  • Repeat the entire procedure to get several sets of data.

Data Collected

Kyle Martin recorded the data. You can refer to F08:People/Martin/Notebook/070912 his lab entry. I've copied the recorded data below:

Mercury

Our Measurements

red clockwise- 695 nm, 695 nm, 697 nm, 696 nm, 696.5 nm,

red counterclockwise- 700 nm, 696 nm, 702 nm, 701 nm, 702 nm

yellow 1 clockwise- 576.5 nm, 579 nm, 577.75 nm, 578 nm, 578 nm

yellow 1 counterclockwise- 579.5 nm, 580 nm, 580.5 nm, 581 nm, 580.5 nm

yellow 2 clockwise- 574.5 nm, 574 nm, 576 nm, 576 nm, 575.5 nm

yellow 2 counterclockwise- 576.75 nm, 576 nm, 578 nm, 577.5 nm, 577.25 nm

green clockwise- 544 nm, 544.5 nm, 545 nm, 545.75 nm, 545.25 nm

green counterclockwise- 545.4 nm, 546.1 nm, 547.5 nm, 546.85 nm, 547 nm

violet clockwise- 435 nm, 435.4 nm, 435.25 nm, 435.9 nm, 435.4 nm

violet counterclockwise- 435.75 nm, 435.6 nm, 435.9 nm, 436.2 nm, 436.1 nm

The True Results

red- 690.75 nm

yellow 1- 579 nm

yellow 2- 577 nm

green- 546.1 nm

violet- 435.8 nm

Hydrogen

Our Measurements

red light clockwise rotation- 656.5 nm, 656 nm, 656 nm, 656 nm, 655.5 nm (n=3)

red light counterclockwise rotation- 656 nm, 660 nm, 659 nm, 659.5 nm, 658.5 nm (n=3)

blue light clockwise rotation- 485.5 nm, 485.5 nm, 485.25 nm, 485.5 nm, 485.1 nm (n=4)

blue light counterclockwise rotation- 486.5 nm, 486.2 nm, 486.5 nm, 486.25 nm, 486.75 nm (n=4)

violet light clockwise rotation- 433.5 nm, 434.1 nm, 433.6 nm, 433.6 nm, 433.7 nm (n=5)

violet light counterclockwise rotation- 434.1 nm, 434.1 nm, 434.25 nm, 434.25 nm, 434.3 nm (n=5)

violet #2 light clockwise rotation- 410 nm, 410.5 nm, 410.1 nm, 409.8 nm, 409.6 nm (n=6)

violet #2 light counterclockwise rotation- 410.25 nm, 410.25 nm, 410.25 nm, 410.2 nm, 410.1 nm (n=6)

The True Results

red- 656.3 nm

blue- 486.1 nm

violet- 434.1 nm

violet 2- 410.2 nm

Deuterium

Our measurements

red light clockwise rotation- 655.2 nm, 654 nm, 656 nm, 654.5 nm, 655.75 nm

red light counterclockwise rotation- 657.5 nm, 658 nm, 658.5 nm, 659.5 nm, 659 nm

blue-green light clockwise rotation- 484.9 nm, 486 nm, 485 nm, 484.9 nm, 485.1 nm

blue-green light counterclockwise rotation- 486.1 nm, 485.5 nm, 486.1 nm, 486.2 nm, 486.1 nm

violet light clockwise rotation- 434.6 nm, 434.3 nm, 433.6 nm, 433.9 nm, 433.5 nm

violet light counterclockwise rotation- 434.1 nm, 433.95 nm, 434 nm, 434.2 nm, 434.2 nm

violet #2 light clockwise rotation- 409.5 nm, 411 nm, 409.3 nm, 409.6 nm, 409.3 nm

violet #2 light counterclockwise rotation- 410 nm, 409.5 nm, 410 nm, 410.2 nm, 410.1 nm

note violet #2 was really faint and hard to see. The measurements on this color were hard to take and there might be some error in that.

Data in tables plus analysis

see comment
Steven J. Koch 03:18, 21 September 2007 (EDT):Jesse (& Kyle): Your data and analysis are spectacular! I am very impressed with the care you showed in taking objective and careful measurements for all of these spectral lines. And I was very excited to see the close match (~0.1%?!) to the expected value of the Rydberg constant, and even possibly the ability to distinguish the difference between Deuterium and Hydrogen. There is something very exciting about the fact that you can measure some manifestation of quantum mechanics so precisely with that old spectrometer! Excellent work!
Steven J. Koch 03:18, 21 September 2007 (EDT):Jesse (& Kyle): Your data and analysis are spectacular! I am very impressed with the care you showed in taking objective and careful measurements for all of these spectral lines. And I was very excited to see the close match (~0.1%?!) to the expected value of the Rydberg constant, and even possibly the ability to distinguish the difference between Deuterium and Hydrogen. There is something very exciting about the fact that you can measure some manifestation of quantum mechanics so precisely with that old spectrometer! Excellent work!

Also see my Excel File which includes

  • Calculations of the Rydberg constant for hydrogen-like atoms (one electron) with infinitely massive nuclei, for hydrogen and for deuterium from physical constants.
  • Calculations of the Rydberg constant from our measured wavelengths.
  • Graphs of measured Rydberg constant vs. excited electron quantum number n
  • I averaged the measured Rydberg constants for all of the average wavelengths of emission lines for hydrogen, from clockwise measured data, and then from counterclockwise measured data. I did the same for all emission lines for deuterium. Then I compared these means to the calculated values of the Rydberg constants for hydrogen and deuterium.
Mercury Clockwise
Red Yellow 1 Yellow 2 Green Violet
695 576.5 574.5 544 435
695 579 574 544.5 435.4
697 577.75 576 545 435.25
696 578 576 545.75 435.9
696.5 578 575.5 545.25 435.4
Average 695.9 577.85 575.2 544.9 435.39
Std. Dev. Of Sample 0.894427191 0.894427191 0.908295106 0.675462804 0.328633535
S/sqrt(N) 0.4 0.4 0.40620192 0.302076149 0.146969385
Accepted Values 690.75 579 577 546.1 435.8
Our Best Estimate 695.9 +/- 0.4 577.85 +/- 0.4 575.2 +/- 0.406 544.9 +/- 0.302 435.39 +/- 0.147
Counterclockwise
Red Yellow 1 Yellow 2 Green Violet
700 579.5 576.75 545.4 435.75
696 580 576 546.1 435.6
702 580.5 578 547.5 435.9
701 581 577.5 546.85 436.2
702 580.5 577.25 547 436.1
Average 700.2 580.3 577.1 546.57 435.91
Std. Dev. Of Sample 2.48997992 0.570087713 0.762397534 0.8243179 0.245967478
S/sqrt(N) 1.113552873 0.254950976 0.340954542 0.368646172 0.11
Accepted Values 690.75 579 577 546.1 435.8
Our Best Estimate 700.2 +/- 1.11 580.3 +/- 0.254 577.1 +/- 0.341 546.57 +/- 0.369 435.91 +/- 0.11
Hydrogen
Clockwise
Red Blue Violet Violet #2
656.5 485.5 433.5 410
656 485.5 434.1 410.5
656 485.25 433.6 410.1
656 485.5 433.6 409.8
655.5 485.1 433.7 409.6
Average 656 485.37 433.7 410
Std. Dev. Of Sample 0.353553391 0.185741756 0.234520788 0.339116499
S/sqrt(N) 0.158113883 0.083066239 0.104880885 0.151657509
Accepted Values 656.3 486.1 434.1 410.2
Our Best Estimate 656 +/- 0.156 485.37 +/- 0.083 433.7 +/- 0.105 410 +/- 0.152
Counterclockwise
Red Blue Violet Violet #2
656 486.5 434.1 410.25
660 486.2 434.1 410.25
659 486.5 434.25 410.25
659.5 486.25 434.25 410.2
658.5 486.75 434.3 410.1
Average 658.6 486.44 434.2 410.21
Std. Dev. Of Sample 1.55724115 0.22192341 0.093541435 0.065192024
S/sqrt(N) 0.696419414 0.099247166 0.041833001 0.029154759
Accepted Values 656.3 486.1 434.1 410.2
Our Best Estimate 658.6 +/- 0.696 486.44 +/- 0.099 434.2 +/- 0.042 410.21 +/- 0.029
Deuterium
Clockwise
Red Blue-green Violet Violet #2
655.2 484.9 434.6 409.5
654 486 434.3 411
656 485 433.6 409.3
654.5 484.9 433.9 409.6
655.75 485.1 433.5 409.3
Average 655.09 485.18 433.98 409.74
Std. Dev. Of Sample 0.838450953 0.465832588 0.465832588 0.716240183
S/sqrt(N) 0.374966665 0.208326667 0.208326667 0.320312348
Accepted Values 656.3 486.1 434.1 410.2
Our Best Estimate 655.09 +/- 0.375 485.18 +/- 0.208 433.98 +/- 0.208 409.5 +/- 0.320
Counterclockwise
Red Blue-green Violet Violet #2
657.5 486.1 434.1 410
658 485.5 433.95 409.5
658.5 486.1 434 410
659.5 486.2 434.2 410.2
659 486.1 434.2 410.1
Average 658.5 486 434.09 409.96
Std. Dev. Of Sample 0.790569415 0.282842712 0.114017543 0.270185122
S/sqrt(N) 0.353553391 0.126491106 0.050990195 0.12083046
Accepted Values 656.3 486.1 434.1 410.2
Our Best Estimate 658.5 +/- 0.354 486 +/- 0.126 434.09 +/- 0.051 409.96 +/- 0.121

see comment
Steven J. Koch 03:25, 21 September 2007 (EDT):So, there are a lot of data to look at, obviously, and I haven't poured over everything, but I do want to post some comments, since you clearly are off to an excellent start. See above for how happy I am with your work on this lab, these are just comments for the future, and not meant to detract from your excellent work:  1. I looked at the Excel sheet, and it appears that you are spot-on with your calculation of standard error of the mean. Great!  2. As for "clockwise" / "counter-clockwise", I think it is excellent that you took each measurement in this fashion and diligently recorded everything. I may not know enough about the instrument: but is it possible to calibrate it so that one or the other is ideal? So you could calibrate it for "clockwise," and then take every measurement from clockwise?  3. Graphs -- Plotting the calculated Rydberg constant versus quantum number is a very good thing to do. For example, it appears that one data point may not be good, perhaps due to the spectrometer.  4. Graphs -- As we talked about in class (I think), you could plot 1/lambda versus (blah) and fit all the data to a line. This perhaps is the best way to get the Rydberg constant (although you would want to make sure that all data points were "good"). We haven't learned how to do this yet, but you may want to give it a shot.  5. Do you know how to comment on whether you are able to tell the difference between Hydrogen and Deuterium ?
Steven J. Koch 03:25, 21 September 2007 (EDT):So, there are a lot of data to look at, obviously, and I haven't poured over everything, but I do want to post some comments, since you clearly are off to an excellent start. See above for how happy I am with your work on this lab, these are just comments for the future, and not meant to detract from your excellent work: 1. I looked at the Excel sheet, and it appears that you are spot-on with your calculation of standard error of the mean. Great! 2. As for "clockwise" / "counter-clockwise", I think it is excellent that you took each measurement in this fashion and diligently recorded everything. I may not know enough about the instrument: but is it possible to calibrate it so that one or the other is ideal? So you could calibrate it for "clockwise," and then take every measurement from clockwise? 3. Graphs -- Plotting the calculated Rydberg constant versus quantum number is a very good thing to do. For example, it appears that one data point may not be good, perhaps due to the spectrometer. 4. Graphs -- As we talked about in class (I think), you could plot 1/lambda versus (blah) and fit all the data to a line. This perhaps is the best way to get the Rydberg constant (although you would want to make sure that all data points were "good"). We haven't learned how to do this yet, but you may want to give it a shot. 5. Do you know how to comment on whether you are able to tell the difference between Hydrogen and Deuterium ?

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