# User:Joseph Frye/Notebook/Physics Junior Lab 307L/BalmerSeries

Steve Koch 04:59, 21 December 2010 (EST):Good notebook, very nice spreadsheet.

## Balmer Series

This lab was performed in the junior laboratory in the UNM physics building on October 25th and November 1st with Alex Benedict. Following the procedure outlined in Dr. Gold's lab manual

## Setup and Equipment

Thanks to David K. O'Hara for the specific model numbers of the equipment used. O'Hara's Lab from 2009

• Adam Hilger London Spectrometer. Serial Number 12610
• Spectrum Tube Power Supply Model SP200 5000V 10 mAmps electro technic products
• Spectrum Tube, Mercury Vapor S-68755-30-K
• Spectrum Tube, Hydrogen S-68755-30-G
• Spectrum Tube, Deuteruim S-68755-30-E

The setup for this experiment is very easy:

1. plug in the power supply

2. put the appropriate tube in the power supply

3. turn on the power supply

4. point the spectrometer at the tube

## Procedure and Data

Procedure:

The goal of this lab is to calculate the Rydberg using the Rydberg Formula :

$\displaystyle \frac{1}{\lambda }=R(\frac{1}{n_{1}^{2}}-\frac{1}{n_{2}^{2}})$

We do this by first measuring the wavelengths in the Balmer series ($\displaystyle n_{1}=2$ ) and then calculate R.

Day 1 - Monday October 25th

The spectrometer must be calibrated to a known sample to ensure meaningful measurements, for this we used mercury vapor. We calibrated the spectrometer to known values of the mercury emission spectrum. We calibrated to the following emission lines of mercury.

• 435.8 nm (violet)
• 546.1 nm (blue-green)
• 577 nm (yellow)
• 579 nm (yellow) - because the two yellow are so close we calibrated only to this one
• 690.75 nm (red)

First we put the mercury vapor lamp into the power supply and allowed it to heat up. We then found the line in the cross hairs we wished to calibrate the spectrometer to. We loosened the screw on the prism and adjusted until the dial agreed with the known value for that particular emission line. We then put the hydrogen tube into the lamp and measured the wavelengths of the emission lines. We did the same for the deuterium bulb. One thing definitely worth noting is that the hydrogen tube gives off a varied spectrum with many many lines that are not characteristic of hydrogen. We measured the strongest (brightest) lines. This was not the case for the deuterium tube however which emits a few distinct lines as we would expect. The data from today is on tab 1 of the spreadsheet.

Day 2 - Monday November 1st

Today instead of physically calibrating the instrument we instead 'corrected' our measurements by first measuring where the known values of the Hg lines were and then fit those values using a linear fit. We then measured the lines for hydrogen and deuterium and used the linear fit to correct our measurements. There is an issue with this equipment where the gears in the instrument effect the measurement given. The way to deal with this is to only turn the dial in one direction each run this is why we did two different linear fits and two different runs for each deuterium and hydrogen, one in each direction. The data from today is on tab 2 of the spreadsheet.

Data

## Results

Known values of the hydrogen spectrum:

• 656.3 nm
• 486.1 nm
• 434.1 nm
• 410.2 nm

Accepted value of R: R=1.09737316E+007 1/m

Measurements from day 1

Hydrogen:

• 653.75 nm
• 486 nm
• 432.78 nm
• 411.4 nm

Deuterium:

• 656 nm
• 484.83 nm
• 433.5 nm
• 409.33 nm

The uncertainty here comes from the standard error of the mean and so all of these values are reported with a 68% confidence interval:

Calculated R using measured hydrogen wavelengths: R=1.0982(24)E+007 1/m

Calculated R using measured deuterium wavelengths: R=1.09885(76)E+007 1/m

Measurements from day 2

Hydrogen:

• 652.57 nm
• 484.44 nm
• 434.93 nm
• 409.27 nm

Deuterium:

• 651.61 nm
• 484.44 nm
• 435.07 nm
• 412.01 nm

The uncertainty here comes from the standard error of the mean and so all of these values are reported with a 68% confidence interval:

Calculated R using measured hydrogen wavelengths: R=1.0996(25)E+007 1/m

Calculated R using measured deuterium wavelengths: R=1.0981(41)E+007 1/m