Physics307L:People/Smith/Notebook/2

=Experiment 2: Balmer Series= (Lab Partner 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 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
Also see my 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.