# Physics307L F09:People/DePaula/Balmer Series

## Equipment

• Spectrometer
• Tubes of Mercury, Hydrogen, Deuterium, and Krypton gas
• Electrical Current Generator (to illuminate the tubes of gas)
• A Positive Attitude SJK 02:18, 13 November 2007 (CST)
02:18, 13 November 2007 (CST)
I think your positive attitude paid off in this lab. The two of you obviously were clicking for this one and got some great data.

## General Goals and Procedure

The goal of this lab is to use a well calibrated spectrometer to collect data about Hydrogen and Deuterium (and in our case Krypton). The hydrogen data we collect will be used to calculate the Rydberg constant. We will then compare and contrast the spectrum of hydrogen, deuterium, and krypton. We begin the lab by calibrating the spectrometer. Here is an excerpt of my lab notebook that details the calibration of the spectrometer.

"Our awesome and amazing TA Devon decides to uncalibrate the apparatus so that we can learn how to properly calibrate. We begin calibration by turning off the lights in the room and running a current through the gas tubes [in this case mercury gas] , producing light. We aim the slit of the spectrometer at the tube. We adjust the brass knob on the spectrometer until it coincides with a known value of a specific line of mercury. We unscrew the prism from its base and pivot it until we see spectral lines in the eyepiece, then adjust it until the cross hairs line up with the spectral line with the same value as the brass knob. We then tighten down the prism, our spectrometer is now calibrated."

## Procedure

We begin the actual experiment by using a hydrogen tube, and measuring the value for every major spectral line. In this case we used the deep violet, violet, teal, and red spectral lines to calculate the Rydberg constant. We decided to use 10 trials to reduce the effect of any one random error. Our results were quite consistent across all trials. Here is a link to our data set which we will refer to for the rest of this summary. Media:REAL BALMER.xlsx. We are measuring an emission spectrum. An emission spectrum is the result of an excited electron falling from a high energy state to a lower state, releasing energy in the form of an electromagnetic wave. The Prism splits these emissions into separate lines. Each of these separate lines corresponds to an electron falling from a different energy state. The wavelength of the emission spectrum is related to the energy of the released photon by the relationship E=hc/(lambda). Where lambda is the wavelength, h is plank's constant, and c is the speed of light.

SJK 02:15, 13 November 2007 (CST)
02:15, 13 November 2007 (CST)
Actually, take a look at wikipedia or elsewhere for discussion of the Rydberg constant and why the nuclear mass makes a difference. Then you can see how much of a difference it makes and whether you expect to be able to see it. That mysterious new line is really crazy, and I want to know what it is.
We do the same procedure with Deuterium. We expect Deuterium to not exhibit different spectral lines, because the only difference between deuterium and hydrogen is the addition of a neutron. We see a new orange spectral line, which is unexpected. The neutron does not add charge to the atom, it only makes it heavier. This extra mass must reduce the kinetic motion of the gas, allowing for the appearance of a separate spectral line.

## Data

1/{\lambda}=R(1/4-1/n^2) The above relationship is what we use to calculate the Rydberg constant. See the excel spreadsheet for the actual numbers.

## Error

SJK 02:16, 13 November 2007 (CST)
02:16, 13 November 2007 (CST)
I think you mean 0.11%. See Anne's page for discussion of how to present final answer the way I would like it.

The error we calculated between our value for the Rydberg constant and the actual value was 11%. our calculated value is 1.098X10^7 +/- 4091. m^-1.