Physics307L:People/Cordova/Matt's Final Lab Report: Difference between revisions
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It must be noted that this equation uses <math>R_\infty</math>, while we are looking for the reduced mass Rydberg constant, which is obtained from<br><br> | It must be noted that this equation uses <math>R_\infty</math>, while we are looking for the reduced mass Rydberg constant, which is obtained from<br><br> | ||
<math>R_M = \frac{R_\infty}{1+m_e/M}</math>Where <math>e_m</math>is the mass of an electron and M is the mass of the atomic nucleus.<br><br> | <math>R_M = \frac{R_\infty}{1+m_e/M}</math>Where <math>e_m</math>is the mass of an electron and M is the mass of the atomic nucleus.<br><br> | ||
It can be seen here why using <math>R_\infty</math> is a good approximation, as <math>m_e</math><<M. | It can be seen here why using <math>R_\infty</math> is a good approximation, as <math>m_e</math><<M.'''[2]''' | ||
==Methods and Materials== | ==Methods and Materials== | ||
Revision as of 23:00, 11 December 2010
Ascertainment of the Rydberg Constant Through Spectroscopy
Experimentalists: Matthew A. Cordova & Roberto Sebastian Rosales
Junior Lab, Department of Physics & Astronomy, University of New Mexico
Albuquerque, NM 87123
Abstract
This lab report will investigate the Rydberg constant, a physical constant which relates to the wavelengths of photons emitted from atoms in an excited state. This will be done through spectroscopy. Specifically, we will be measuring the wavelength of photons emitted by Hydrogen and Deuterium gas observed as spectral lines isolated through diffraction. Although this can be seen as a dated method compared to modern science, the results obtained in this lab were quite acceptable. The reduced mass Rydberg constant for Hydrogen and Deuterium were found to be [math]\displaystyle{ 1.0977(7)*10^7m^{-1} }[/math] and [math]\displaystyle{ 1.0990(2)*10^7m^{-1} }[/math], respectively. The accepted values for Hydrogen and Deuterium are [math]\displaystyle{ 10967758.3406m^{-1} }[/math] and [math]\displaystyle{ 10970746.1986m^{-1} }[/math], respectively.
Introduction
As previously mentioned, atoms in an excited state emit photons when they go back down to a more stable energy level. A more accurate description, however, would be that the electrons in an atom are what reach excited levels, and the energy lost in the transaction to a lower (more stable) energy state is in the form of an emitted photon. Since the energy levels are defined as integers, there are discrete energies, i.e. wavelengths, that this photon may have. The Balmer series, first explored by Johann Balmer, deals with excited energy levels transitioning down to the n=2 state. To observe this process, my lab partner Sebastian and I will excite Hydrogen and Deuterium gas and observe the photons emitted through a constant deviation spectrometer. By sending the emitted photons through a diffracting medium, we can isolate the wavelengths and use Rydberg's equation to determine the corresponding constants for Hydrogen and Deuterium. Johannes Rydberg crafted his equation strictly from empirical data. No theory went into its conception.[1] It is expressed as
[math]\displaystyle{ \frac{1}{\lambda} = R_\infty \left(\frac{1}{n_1^2}-\frac{1}{n_2^2}\right) }[/math]
It must be noted that this equation uses [math]\displaystyle{ R_\infty }[/math], while we are looking for the reduced mass Rydberg constant, which is obtained from
[math]\displaystyle{ R_M = \frac{R_\infty}{1+m_e/M} }[/math]Where [math]\displaystyle{ e_m }[/math]is the mass of an electron and M is the mass of the atomic nucleus.
It can be seen here why using [math]\displaystyle{ R_\infty }[/math] is a good approximation, as [math]\displaystyle{ m_e }[/math]<<M.[2]
