# Physics307L:People/Gooden/Notebook/071008

BALMER SERIES

## Set up

• We begin by calibrating the spectrometer, using three spectral lines of Mercury(Hg):
• 435.8 nm Violet
• 546.1 nm Green
• 577.0 nm Yellow 1
• This is done by removing the black metal covering for the prism. Then we rotated the dial until we were at the first wavelength (Violet) and adjusted the prism till the spectral line was as close to center on the crosshairs as possible.Then we moved onto the next wavelength, the 546.1 nm Green line. Here we adjusted the prism again till the green line was centered on the crosshairs. Finaly, we repeated this process for the Yellow 1 577.0 nm line.
• After the calibration we set the dial back to zero and turned the dial up until through the viewing scope we were able to see a particular spectral line. The results for doing this for our three test wavelengths are given below. They are fairly accurate for how fine the dial is and how accurate it is to read the wavelenght off of the dial.
• For Mercury we find lamda for the spectral lines to test the calibration to be:
       Violet:       436.4 nm
Green:        548.1 nm
Yellow 1:     580.2 nm


## Procedure

• Step 1:Collect all necessary equipment
• "Constant Deviation" Spectrometer
• Several Gas Tubes: Mercury Tube,Hydrogen Tube,Deuterium Tube
• Spectrum Tube Power Supply
• Step 2:Complete the calibration of the spectrometer as described above in the Set Up
• Step 3:Place the gas tube with the desired gas into the connectors of the Spectrum Tube Power supply.
• Step 4:Turn on Spectrum Tube Power supply and allow gas tube several minutes to warm up.
• Step 5:Position Spectrometer with Gas Tube and Power Supply propped up(6-8 in) to be

level with the Spectrometer and placed on the opposite end from the eye piece.

• Step 6:Start with the dial turn down to the zero level, and the rotating it counter-clockwise until you see the spectral lines begin to appear in the viewing scope.
• Step 7:Once the spectral line is centered on the crosshairs, record the wavelength off of the dial.
• Step 8:Continue to next spectral line and repeat step 7.
• NOTE: You want to make sure to not turn the dial back clockwise while taking measurments. There is slippage in the gears and by turning it back opposite to the way you were moving it can cause it to unalign and create errors.
• Step 9:Repeat steps 7 and 8 for next Gas Sample

## Data

• Hydrogen
Color Violet 1 nm Violet 2 nm Blue nm Red nm
Quantum Number n = 6 n = 5 n = 4 n = 3
Measurment
1 410.5 432.9 486.5 660.9
2 410.0 433.2 486.9 661.1
3 409.5 433.6 487.2 660.9
4 410.5 433.5 487.8 660.7
5 410.5 433.6 486.5 660.5
6 410.25 433.2 486.5 660.5
7 410.0 433.6 486.5 660.7

• Deuterium
Color Violet 1 nm Violet 2 nm Blue nm Red nm
Quantum Number n = 6 n = 5 n = 4 n = 3
Measurment
1 410.0 432.1 486.0 660.0
2 410.0 433.1 486.1 660.1
3 409.75 433.2 486.5 660.1
4 409.75 433.1 486.5 660.0
5 409.75 433.1 486.2 660.0
6 410.0 433.1 486.2 660.0
7 410.0 433.1 486.6 660.0
• Neon
Color Yellow nm Red nm
Quantum Number n = 4 n = 3
Measurment
1 580.3 642.0
2 585.8 642.0
3 585.6 642.1

## Analysis

$R=\frac{1}{\frac{\lambda}{4}-\frac{\lambda}{n^2}}$

• Using excell to find the mean wavelength for each color of Hydrogen and Deuterium, we find:
Color Violet 1 nm Violet 2 nm Yellow nm Red nm
Quantum Number n = 6 n = 5 n = 4 n = 3
Hydrogen
Mean 410.1786 433.3714 486.8429 660.7571
STD Deviation .3740 .2752 .5028 .2225
Deuterium
Mean 409.89 433.12 486.40 660.02
STD Deviation .1336 .3860 .2309 .0487
• Using the formula given above we find that the Ryberg Constant for each color of Hydrogen and Deuterium is:
Color Violet 1 nm Violet 2 nm Yellow nm Red nm
Hydrogen
Rydberg R (m^-1) $1.0971\times 10^7$ $1.0988\times 10^7$ $1.0955\times 10^7$ $1.0897\times 10^7$
Deuterium
Rydberg R (m^-1) $1.0978\times 10^7$ $1.0994\times 10^7$ $1.0965\times 10^7$ $1.0909\times 10^7$
• Now taking the mean of the measured Rydberg Constant R for each element, we find:
• For Hydrogen: $R_H=\left(1.0953 \pm .0039\right)\times 10^7 {m^-1}$
• For Deuterium: $R_H=\left(1.0962\pm .0037\right)\times 10^7 {m^-1}$

## Results

• The accepted value according to Wikipedia of the Rydberg Constant for Hydrogen is
$R_H = 10 967 758.341 \pm 0.001\,\mathrm{m}^{-1} \$

And thus we can see that our value found by this experiment is in good approximation to this accepted value, and we are reporting our value of the Rydberg Constant for Hydrogen as:

• For Hydrogen: $R_H=\left(1.0953 \pm .0039\right)\times 10^7 {m^-1}$
• Also, the accepted value of the Ryderbeg constant for Deuterium according to The Reviews Of Modern Physics(1)

$R_D=\left(1.09707 \pm .7\right)\times 10^7 {m^-1}$ And thus we can see that our value found by this experiment is in good approximation to this accepted value, and we are reporting our value of the Rydberg Constant for Deuterium as:

• For Deuterium: $R_D=\left(1.0953 \pm .0039\right)\times 10^7 {m^-1}$

## References

• Reviews of Modern Physics.A New Table of Values of The General Physical Constants.Raymond T. Birdge. Vol 13.October 1941.