User:Arianna PregenzerWenzler/Notebook/Junior Lab/2008/09/17
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Balmer Series Lab^{SJK 00:04, 6 October 2008 (EDT)}Objectives(directly quoted from lab manual)
Equipment^{SJK 12:03, 19 September 2008 (EDT)} *"constantdeviation" spectrometer, mercury, hydrogen and deuterium bulbsInitial SetupTurned on mercury tube. (we don't even really know if it is mercury. ) To start we explored out spectrometer to understand the purpose and function of the numerous dials. One dial near the prism slowly rotated the prism that we may control the wavelength that passes through the scope. To take a measurement of the wavelength we simply line of the crosshairs with our desired color and read the measurement off of the dial which is given in nano meters. Note: if you look down at the data we collected, especially on the first day, you will see on quite a few occasions one of us misread the dial. The person recording the data usually caught this fairly quickly because that person would notice that the person making the measurments had just given a value for the wavelenght that was very inconsistant with previous or expected values. I would suggest taking a close look at the dial that gives your measurment and make sure you know how to read it before getting started.
Another dial near the end of the apperatus opens and closes the slit alowing more or less light in from the light tube. We can minimize the width of the bright wavelengths to get better precision. To veiw the less visible wavelengths we must sacrafice precision so that we can see the color band. The structure of the spectrometer keeps keeps the incident ray and the axis of the anaylizing telescope fixed at 90degrees. When I first read the lab manuel and it said "that for spectral anaylysis of light is to rotate the prism relative the the incident light keeping the incident ray and the axis of the anaylizing telescope fixed at a 90 deg angle," I wondered how this was to be accomplished. Then I saw the spectrometer.
So now it is September 24, Dan and I took our data and began to put it in MATLAB and analize it and ran into a problem. We thought that we just used our spectrometer to read off values for mecury and from that we could create a linear curve of values given our insterment and a linear curve of values for accepted values and determine from there how to correctly inturpert our hydrogen and deuterium data. Wrong, we needed to take the accepted mercury values and set the dial on the spectrometer to one of those values then rotate the prism until the correct band of color was aligned in the crosshairs. Here is a picture of the prism whit its cap off.
Calibration of the Spectrometer: deep purple: can't see the deep purple with the cap off purple: 435.8nm set dial exactly on this value and then rotated prism until purple was directly in the crosshairs green: 546.1nm set dial to this wavelength and the crosshairs are on green but off to one side of center. So what do we do now because if we rotate the prism at this point we undo the adjustment we made on purple? At this point we check the other accepted values (yellow:577nm, 2nd yellow:579nm, red:690.75nm). For accepted values of the mercury spectrum the crosshairs land on the band of color that corresponds to that value, though not necessarily in the center. We call this good enough since obviously our spectrometer is not going to be an exact match to the measurments made by another insturment. Now with a calibrated spectrometer, we pop in the hydrogen bulb and prepare to take a new series of measurments. Calibration of the Spectrometer
Arianna Mecuryenetered data in MATLAB, called 2nd yellow orange ^{SJK 23:51, 5 October 2008 (EDT)}Trial 1 Deep violet 405.8nm note: the 1st four of these (until 2nd yellow) done with the overhead lights on Purple 437.2nm Green 549.5nm 1st yellow 582.5nm 2nd yellow (looks orange) 661.55nm (Misread the dial. Supposed to be 615.5) red  709.0 Trial 2 Deep violet 405.8nm Purple 437.8nm Green 555.15nm 1st yellow (1st try was 558.25nm tried again since value was far off from previous) 585.5nm 2nd yellow (looks orange) 616.0nm red  710.4nm Trial 3 Deep violet 405.3nm Purple 437.2 Green 554.0 1st yellow 587.0 2nd yellow (looks orange) 615.5 red  712.0 Daniel MecuryTrial 1 Deep violet 406.5nm Purple 437.4nm Green549.6nm 1st yellow582.8nm 2nd yellow608.8nm Red709.9nm Trial 2 Deep violet 406.1nm Purple 437.2nm Green 554.95nm 1st yellow 558.3nm (redone, because he misread dial, actually 581.1nm) 2nd yellow 610.0nm Red 705.0nm Trial 3 Deep violet 406.1nm Purple 437.3nm Green550.0nm 1st yellow582.5nm 2nd yellow609.0nm Red708.0nm
the Hydrogen SpectrumArianna Hydrogenfrom looking at a picture of the hydrogen emission (wiki entry on hydrogen) it looks like hydrogen has 4 bands of color in the visible spectrumhydrogen. The colors are 2 purples, a cyan and a red. From this information and looking at the expected values for the hydrogen spectrum hydrogen spectral seriesit looks like the color band we called yellow for hydrogen should not be used as part of our calculations. When I wrote this I didn't realize that our data was bad, so now when we take new data we will only record values for the 2 purples, th cyan and the red. Arianna Trial 1(9/24): Deep violet 410.2nm Purple 434.7nm Cyan 486.9nm red  665.5nm Trial 2 (9/24): Deep violet 409.9nm Purple 434.6nm Cyan 487nm red  666.0nm Trial 3 (9/24): Deep violet 410nm Purple 434.7nm Cyan 487nm red  666.0nm
Trial 1(9/24): Deep violet 409.9nm Purple 444.6nm (note I assuming a mistype and 434.6nm actual)^{SJK 23:53, 5 October 2008 (EDT)}Cyan 486.9nm red  665.0nm Trial 2 (9/24): Deep violet 410.2nm Purple 434.6nm Cyan 487.0nm red  666.0nm Trial 3 (9/24): Deep violet410.3nm Purple434.2nm Cyan487.0nm red 666.5nm the corresponding n values are n=3 for red, n=4 for cyan, n=5 for purple, n=6 for deep purple ^{SJK 23:58, 5 October 2008 (EDT)}Trial 1 Deep violet 411.9nm Purple 436.9nm Cyan 489.5nm yellow 594.5nm red  671.5nm Trial 2 Deep violet 412.0nm Purple 437.1nm Cyan 490.0nm yellow 596.5nm red  671.0nm Trial 3 Deep violet 411.8nm Purple 436.3nm Cyan 489.5nm yellow 596.0nm red  671.0 Daniel HydrogenTrial 1 Deep violet413.3nm Purple 437.0nm Cyan488.5nm yellow 589.0nm (definition of this line is lacking, so this line is a little more open to inturpretation) Red674.0nm Trial 2 Deep violet 413.5nm Purple 436.5nm Cyan490.4nm yellow 596.0nm Red675.0nm Trial 3 Deep violet413.6nm Purple 437.3nm Cyan489.7nm yellow 589.0nm Red670.0nm The Deuterium SpectrumArianna Trial 1 (9/24): Purple 434.2nm Cyan 486.5nm red  664nm Trial 1 (9/24): Purple 433.6nm Cyan 486.4nm red  665nm Trial 1 (9/24): Purple 433.4nm Cyan 486.5nm red  664.5nm
Trial 1 (9/24): Purple 434.5nm Cyan 486.6nm red  665nm Trial 2 (9/24): Purple434.2nm Cyan 486.7nm red  665.0nm Trial 3 (9/24): Purple433.9nm Cyan486.7nm red  665.0nm the corresponding n values are n=3 for red, n=4 for cyan, n=5 for purple,
Arianna DeuteriumTrial 1 Purple 435.2nm Cyan 487.5nm yellow 590.5nm 2nd yellow 612.0nm Red 667.0nm Trial 2 Purple 434.7nm Cyan 488.4nm yellow 591.0nm 2nd yellow 612.5nm Red 666.5 Trial 3 Purple 435.8nm Cyan 487.6nm yellow 590.8nm 2nd yellow 612.8nm Red666.5 Daniel DeuteriumTrial 1 Purple434.8nm Cyan488.0nm yellow 586.0nm 2nd yellow606.8nm Red669.0nm Trial 2 Purple434.7nm Cyan487.6nm yellow585.9nm 2nd yellow614.0nm Red669.0nm Trial 3 Purple434.3nm Cyan488.2nm yellow587.0nm 2nd yellow608.2nm Red665.0nm
Notes/ObservationsFor the yellow band (hydrogen), and both yellow and 2nd yellow (deuterium), there was not a sharply defined line that correlated to these colors, rather in both cases there was a blury band of light that seemed to be sharpest at some point. Therefore, if for no other reason then our readings of these bands was to some degree a matter of personal interpretation, we may find that we do not want to use the values for these color bands in our final calculations. The lab manuel mentions that additional faint lines in the mercury spectrum may be the cause of impurties or from other molecular behavior. Are these large undefined bands of color part of the Hydrogen/Deuterium spectrum or are they caused by something else? Look up hydrogen and deuterium spectrums and compare accepted colors(and values) to observed values.
the way it splits the incoming beam of light into its different wavelengths...
energy quantized, photons emitted at specific frequencies... *Dan and*Arianna PregenzerWenzler 18:54, 17 September 2008 (EDT): Analysis
Off the top of my head (with details doubled checked using my physics 330 book, "Quantum Physics...", Eisberg and Resnick) the physics in this lab is as follows. When we the mercury bulb into the lamp and pluged it in we added energy (in the form of electrity) to the mecury atom causing large numbers of electrons to leave their groundstate (lowest energy state, n=1) and enter an excited state. Once in an excited state the electrons want to return to lower energy and do so be releasing their energy in the form of photons. These energy emmisions are quantized (only specific values) of the form E= n*h*neu; where neu is the frequency, h is Planck's constant, and n is the principle quantum number. What we see as visible light is actually EM radiation in the spectrum corresponding to frequencies aproximately between 7.5 to 4.3 *10^14 Hz (or wavelengths between 700nm(red) and 400nm(violet). When the "white" light from from the mecury (or hydrogen, or deuterium) bulb passes through the prism in the spectroscope it is seperated into its different componets (bands of color) according to their diferent engeries charactized by different frequencies because differet frequencies have different indexes of refraction inside this medium (the prism). By using the spectroscope we can identify the values of the energy being emmited in the visible range by the atom in question by reading off the wavelength associated with a particular band of color.
This comming week in lab we need to look at the data of the known mercury spectrum and use it to calibrate the readings of our spectroscoope using the data we took using the mercury bulb. This means we need to figure out if our spectroscope says the red band is at 655nm aproximately how far off from the actual accepted wavelength of this red band are we. Once we have calibrated our spectroscope we can anaylize our hydrogen and deuterium data and get a good aproximation of the wavelenghts of the bands of color we observed in their spectrums. With this information we shoul be able to look up the value on n that corresponds to the emmision of photons with these wavelenghs, and with the values of n we should be able to determine a good aproximation for R, the Rydberg constant.*Arianna PregenzerWenzler 23:56, 21 September 2008 (EDT):
In class my lab partner and I put our data into MATLAB, actually he entered and manipulated it (I read it to him). We used MATLAB to compute the average values of our measured wavelenghts for the different color bands of Hydrogen and Deuterium, and also the standard deviation, from these values of wavelength and using the appropriate values for n (found on wiki see lab notebook link), We calculated the Rydberg constant for Hydrogen and Deuterium. Dr Koch also took the time to put some of our data into Excel (see attachments at botom, though they are rather incomplete) in the form of a linear plot the slope of which line was equal to our experimental value for R. Something interesting happened here; from the averaged values of our data in MATLAB we had been able to caluculate a value for R that appeared to be quite close to its accepted value, but when we looked at the slope of our data plotted linearly (slope=R) we found that this form of our experimently calculated R was unacceptably far from its accepted value. We didn't really understand what happened here but when Dr Koch forced the line connecting our data to also go through zero, our R value as estimated from the slope of the line looked much better.
