User:Arianna Pregenzer-Wenzler/Notebook/Junior Lab/2008/09/17

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Objectives
(directly quoted from lab manual)
 * Review basic atomic physics
 * Calibrate an optical spectrometer using the known mercury spectrum
 * Study the Balmer Series in the hydrogen spectrum
 * Determine the Rydberg constant for hydrogen
 * Compare hydrogen with deuterium

Equipment
*"constant-deviation" spectrometer, mercury, hydrogen and deuterium bulbs

Initial Setup
Turned 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

 * remember: any measurments taken/data collections need to be repeated at least 3X so that I have a measure of my error

Arianna Mecury
enetered data in MATLAB, called 2nd yellow orange

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 Mecury
Trial 1 Deep violet- 406.5nm Purple- 437.4nm Green-549.6nm 1st yellow-582.8nm 2nd yellow-608.8nm Red-709.9nm 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 Green-550.0nm 1st yellow-582.5nm 2nd yellow-609.0nm Red-708.0nm

Arianna Hydrogen
from 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

Daniel

Trial 1(9/24):

Deep violet- 409.9nm

Purple- 444.6nm (note I assuming a mistype and 434.6nm actual)

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 violet-410.3nm

Purple-434.2nm

Cyan-487.0nm

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

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 Hydrogen
Trial 1 Deep violet-413.3nm Purple- 437.0nm Cyan-488.5nm yellow- 589.0nm (definition of this line is lacking, so this line is a little more open to inturpretation) Red-674.0nm Trial 2 Deep violet- 413.5nm Purple- 436.5nm Cyan-490.4nm yellow- 596.0nm Red-675.0nm Trial 3 Deep violet-413.6nm Purple- 437.3nm Cyan-489.7nm yellow- 589.0nm Red-670.0nm

The Deuterium Spectrum
Arianna

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

Daniel

Trial 1 (9/24):

Purple- 434.5nm

Cyan- 486.6nm

red - 665nm

Trial 2 (9/24):

Purple-434.2nm Cyan- 486.7nm

red - 665.0nm

Trial 3 (9/24):

Purple-433.9nm

Cyan-486.7nm red - 665.0nm

the corresponding n values are n=3 for red, n=4 for cyan, n=5 for purple,

Arianna Deuterium
Trial 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 Red-666.5

Daniel Deuterium
Trial 1 Purple-434.8nm Cyan-488.0nm yellow- 586.0nm 2nd yellow-606.8nm Red-669.0nm Trial 2 Purple-434.7nm Cyan-487.6nm yellow-585.9nm 2nd yellow-614.0nm Red-669.0nm Trial 3 Purple-434.3nm Cyan-488.2nm yellow-587.0nm 2nd yellow-608.2nm Red-665.0nm

Notes/Observations
For 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...
 * mention, purpose of prism...
 * mention, why seperate bands...

*Dan and*Arianna Pregenzer-Wenzler 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.
 * Review basic atomic physics

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.


 * In this lab we want to look at the Balmer series for hydrogen and determine the Rydberg constant for hydrogen. The Balmer series looks at photons emmited with wavelengths in and close to the visible range by electrons starting at an excited state n>2 (ie:3,4,5,....) and ending at n=2.

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 Pregenzer-Wenzler 23:56, 21 September 2008 (EDT):

After entering the average values of our wavelengths from our corrected calibrated spectrometer and their corresponding n values into a MATLAB program, written by Daniel we calculated a average R constant. Then we go into the consistancy of our data and looked at graphing it in both excell and matlab and what our error ment. Daniel,and*Arianna Pregenzer-Wenzler 19:03, 24 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.


 * [[Image:Balmer Series(Arianna and Dan).xlsx]]
 * [[Media:Balmer Series(Arianna and Dan).xlsx]]


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