User:Michael R Phillips/Notebook/Physics 307L/2008/10/29: Difference between revisions
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<math>n_{red}=3 | <big><math>n_{red}=3</math> | ||
<math>n_{cyan}=4</math> | |||
<math>n_{violet1}=6</math> | |||
<math>n_{violet2}=7</math></big> | |||
Revision as of 14:19, 5 November 2008
 Balmer Series
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Balmer SeriesIntroduction & SafetyIn this lab, we will be using a very old Constant Deviation Spectrometer to measure the Rydberg constant based on the spectra of Hydrogen and Deuterium, and also the difference between the spectral wavelengths for these two, roughly following this lab manual. As for safety, the main thing is don't get electrocuted. This means turning off and unplugging the lamp power before removing or inserting a new bulb. Other important things to note, for equipment safety rather than our own, is that we should never touch the prism because we could easily damage it with fingerprints and that we should be very careful not to break the bulbs. CalibrationBefore we do any real data taking, we need to perform a simple calibration for our instrument. For this, we will use the given values of wavelengths (λ) and colors to match to our corresponding wavelengths and colors. In the end of the experiment, we will use this data to account for a kind of "calibration error" that will appear in every part of our data. Here is the data we took for initial calibration:
Along with the lines with given wavelengths, we found in our spectrum several low intensity lines that the lab manual indicated were from impurities in the sample. We also saw clearly the blue-green line that the manual directs us to skip. After taking all of this calibration data, we can use the average between our two values for each color and compare these to the values that were supplied to us so that we will have a good correction for the Hydrogen and Deuterium spectral data. Note: after taking this data and guessing as to what the method would be for calibration, we discovered that it was completely wrong! The correct way is to fix the prism rotation so that it gives us a perfect value for one of the middle wavelengths (like yellow or green). This will automatically give us good values for the rest of the experiment. This was done properly, calibrating to "yellow1" (579.0nm), before taking our actual data below. DataFor Hydrogen:
Ηελλο ωηατ αρε ψου δοινγ. AnalysisWe will use all of this data in this equation [math]\displaystyle{ \frac{1}{\lambda}=R(\frac{1}{2^2}-\frac{1}{n^2}), n=3,4,5,... }[/math] which relates our measured wavelengths, λ, to the Rydberg constant, R, with a couple of constants. The only thing we need to figure out from here is which color corresponds to which quantum number, n. The easiest way to handle all of our data is to plot λ vs n and determine a slope, a part of which will be R-dependent. The function that we will use is: [math]\displaystyle{ \lambda(n)=\frac{4n^2}{R(n^2-4)}, n=3,4,5,... }[/math]
[math]\displaystyle{ n(\lambda)=\sqrt{\frac{4\lambda R}{\lambda R-4}} }[/math] which we use to decide which n corresponds to the red wavelength. From this, we found
[math]\displaystyle{ n_{cyan}=4 }[/math] [math]\displaystyle{ n_{violet1}=6 }[/math] [math]\displaystyle{ n_{violet2}=7 }[/math]
[math]\displaystyle{ \frac{1}{\lambda}=R(\frac{1}{m^2}-\frac{1}{n^2}), m=1,2,3,... , n=2,3,4,... , n\gt m }[/math] that is said to be more accurate (the first equation was discovered empirically while this one was a modified version to account for all wavelengths and is reinforced by Bohr's work). However, for our purposes, assuming m=2 and n=3,4,5,... is perfectly okay.
We will then compare our values of R to the actual value: [math]\displaystyle{ R_{accepted}=1.0967758\times10^7m^{-1} }[/math] using a percent error formula [math]\displaystyle{ %Error=\frac{|Accepted-Measured|}{Accepted}\times100 }[/math] | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
