# User:Randy Jay Lafler/Notebook/Physics 307L/2010/11/15

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Steve Koch 05:47, 21 December 2010 (EST):Good notebook.

## 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.

Everything up to the calculations part of this lab is the same as Emran's notebook.

### 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

• 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

### Calculations

We measured a Rydberg constant for Hydrogen and for Deuterium. We did not average these two numbers together because the constant for hydrogen and for deuterium should be different. The Rydberg constant depends on the mass of the nucleus, which is larger for deuterium because of the neutron it has in the nucleus.

• We determined the Rydberg constants by using the following equation.
$1/wavelength=R*(1/2-1/n^2)\!$
• We then plotted one over our wavelengths so that the slope of the line is the Rydberg constant.
$R=\frac{1/wavelength}{1/2-1/n^2}\!$
R for hydrogen and deuterium
$R_H=1.10(4)*10^7/m\!$
$R_D=1.104(5)*10^7/m\!$

### Error

The accepted value for the Rydberg constant for hydrogen is 1.0974*10^7/m. The range of our value for hydrogen is 1.06*10^7/m to 1.14*10^7/m. The accepted value is within one standard error of our data, and the best answer we obtained is very close to the accepted value. Our data for the deuterium had an even smaller standard error than we had for the hydrogen constant. In fact, the error is so small you cannot differentiate our data points from the fit line points and you cannot see the vertical error bars in our plot. I believe, therefore, that we did good measurements. At first, we had a hard time seeing the spectral lines for the hydrogen. We saw much more lines than there should have been, and it was hard to determine which lines were actual spectral lines. We decided to choose the lines that were the sharpest and brightest. This is why we calculated a wavelength for a yellow spectral line for the hydrogen and even for the deuterium that does not actually exist. The manual said that we should at least see for lines for the hydrogen bulb, and we only saw 3 lines distinctly. We choose an incorrect yellow spectral line because it looked the next brightest after the three we determined correctly. We also had a some extra, false spectral lines for the deterium and assumed that if the hydrogen had a yellow spectral line so would the deuterium. In addition to this, we adjusted the last measurement in calibration factors from -9 to 2nm to match the rest of our calibration measurements. We did this both because it does not make sense that the calibration would jump from a positive to a negative value, and because the -9 for the red, 690nm calibration measurement was distorting our end measurement for the rydberg constant. We noticed that after making the common sense change from -9 to 2 nm our measurements were much more accurate. We believe that we must have measured the last calibration point incorrectly. The spacing for the larger wavelengths on the wavelength positioner is smaller and we must have made a mistake measuring it.

### Acknowledgments/citations

Emran for being by lab partner again.