User:David J Weiss/Notebook/notes Balmer

=Blamer Series=

In this experiment we will find through experimentation the value of the Rydberg Constant through the observation of spectral lines of the Hydrogen Atom and the Deuterium Atom. To do this we will excite the atoms of the Hydrogen and Deuterium by means of electric stimulation of the gas to excite the electrons in the gas to higher energy levels. When the electrons go back into the original energy levels they emit a photon whose wavelength is equal to the amount of energy of the electron.

Equipment

 * Constant-Deviation Spectrometer
 * Spectrum Tube Power Supply Model SP200 5000V
 * Spectrum Tube, Mercury Vapor S-68755-30-K
 * Spectrum Tube, Hydrogen S-68755-30-G
 * Spectrum Tube, Deuterium S-68755-30-E

Setup
The set up of this lab is as follows:
 * Position the Constant-Deviation Spectrometer so you can have to view the Gas tubes
 * Adjust the Height of the Spectrum Tube Power Supply so you can view the tubes through the eyepeace of the Spectrometer
 * Place the tube into the Spectrum Tube Power Supply
 * Plug the spectrum Tube Power Supply in and turn it on
 * Adjust the prism so you can view the spectral lines of the Mercury Vapor

Safety
This lab has the following safety concerns:
 * Electrical Shock: due to the fact that the gasses are excited through electrical means there is a safety concern that the equipment due to the fact that it runs on electricity will shock you
 * Glass Tubes: glass may break and cut your skin and also make sure you do not inhale the gasses contained within the tubes
 * Mercury Gas: toxic gas that can cause bodily harm if inhaled
 * Care of the interments
 * Don't Drop things on your self

Day 1

 * Worked with Elizabeth Allen and thanks for all the help
 * First we went through the safety brief with Dr Koch and Pranav Rathi
 * Then we set up the lab we had to use several books to adjust the height of the lamp in relation to the Spectrometer
 * Then we got the equipment and started to calibrate the Spectrometer with mercury vapor by adjusting the prism and then adjusting the screw drive till we were able to view the mercury lines. We also had to adjust the width of the slit while calibrating the spectrometer.  While calibrating the spectrometer we would start with the green at 546.1nm then calibrated the yellows from there a yellow line at 576.4nm the manual says it should be at 577 nm an error of about .6 nm, another yellow line at  578.5nm which is off by .5nm, and a red line at 701nm which is not what the manual says should be at 690.75 an error of about 10.25nm.  We then went to look at the violet at 435.9nm which was off the manuals by .1nm, the second violet line was at 404.5nm the book value is 404.7nm a difference of .2nm.
 * While adjusting the screw drive we needed to be careful of the slop or play in the gears and make sure to keep the spectral lines in the cross hairs of the eye peace
 * We decided to use a narrow light instead of a wide light sacrificing the intensity of the light for a better resolution of the spectral lines
 * After we calibrated the Spectrometer we then measured the spectral lines of the hydrogen gas below. The first line we observed was the violet line followed by the blue-green line then the red.  We were a little confused about what the actual spectral lines were but we deiced upon two in the range of yellow spectral lines.
 * We measured the Deuterium the first spectral line we observed was the red line, followed by the viloet line, then the blue-green line. A yellow line was observed followed by an orange line but both of them were more faint than the others.

Day 2

 * On day two i worked with Elizabeth Allen again.
 * Used several books again to get the proper height of the lamp and turned on the lamp to let it warm up for 5 minutes. After that we opened the slit using the screw drive so i can calibrate the scope.
 * We then adjusted the prism using the mercury vapor to calibrate the scope starting with the green spectral line at 546.1 nm. after finding the green spectral line we then went to the violet at 435.9nm which is off from the expected value by .1nm.  After seeing the violet we went back to the green and found the red at 697nm off about 7.75nm.  Then the yellow lines at 579.7nm off about .7nm and the 2nd yellow line at 577 which is the value given in the manual.
 * After calibrating the spectrometer we then went to measure the spectral lines for hydrogen. The first line was the violet. We measured it 5 different times. Then repeated for the red, then the yellow and then the orange ending the hydrogen with the blue green spectral line.
 * We then started to measure the spectral lines of the Deuterium starting with red but upon looking we could only find the red and the blue-green spectral line. We could not find any other spectral so we only have the readings for the red and blue-green for the Deuterium.

Hydrogen Data
Violet: 434.1nm

Blue-Green :486nm

Red: 660nm

Yellow: 580.8nm

Orange: 604.8nm

Deuterium
Red: 659.1nm

Violet: 434.3nm

Blue-Green: 486.3nm

Yellow: 584.1nm

Orange: 618.8nm

Hydrogen
Violet: 433.8nm,  434nm,  433.9nm,  434.2nm,  434.3nm

Red: 657.6nm,  657.0nm,  657.6nm,  577.7nm,  657.4nm

Yellow: 582.4nm,  582.7nm,  582.6nm,  582.9nm,  582.4nm

Orange: 603.3nm,  604.0nm,  603.9nm,  603.7nm,  603.6nm

Blue-Green: 486.3nm,  486.0nm,  486.2nm,  485.9nm,  485.9nm

Deuterium
Red: 657.8nm,  656.7nm,  657.2nm,  658.2nm,  656.6nm

Orange:

Yellow:

Blue-Green: 485.2nm,  485.6nm,  485.2,  485.2nm, 485.2nm

Violet:

Hydrogen
Red: 657.88+/-0.43nm

Orange: 603.88+/-0.2nm

Yellow: 582.3+/-0.31nm

Blue-Green: 486.05+/-0.07nm

Violet: 434.05nm+/-.07nm

Deuterium
Red: 660.6+/-3.06nm

Orange: 618.8nm

Yellow: 584.1nm

Blue-Green: 585.45+/-.18nm

Violet: 434.3nm

Calculating the Rydberg Constant
Rydberg formula for hydrogen:

$$\frac{1}{\lambda }=R_{H}(\frac{1}{2^{2}}-\frac{1}{n^{2}})$$

Rydberg formula for Hydrogen like Elements:

$$\frac{1}{\lambda }=RZ^2(\frac{1}{2^{2}}-\frac{1}{n^{2}})$$(where Z is the Atomic Number)

Using this formula(from Wikipedia) you can calculate the approximate value for the Rydberg Constant by knowing the transitions from the excited levels to the non excited states(ground states) by the following calculations:

$$\frac{\frac{1}{\lambda }}{(\frac{1}{2^2}-\frac{1}{n^2})}=R_{H}$$

where $$R_{H}$$ is the Rydberg Constant for hydrogen, $$\lambda$$ is the observed wavelength, and n is the excited energy state that the electron was in. You can find out what states that the electron was in by looking that up on a table i used the Wiki page on Blamer Series Wiki Article (Steve Koch 02:21, 29 September 2009 (EDT):Good citation) and looked at the lines for the Blamer series. The n=5 line represents the violet color that is emitted, the n=4 line represents the blue-green line that's emitted. The n=3 represents the red line that is emitted.

Rydberg Constant for Hydrogen($$R_{H}$$)

 * $$\frac{(\frac{1}{657.88nm})}{(\frac{1}{2^2}-\frac{1}{3^2)}}$$ = $$R_{H}$$ for the red spectral line = 1.0944245+/-.00071$$*10^{7}m^{-1}$$
 * $$\frac{(\frac{1}{486.05nm})}{(\frac{1}{2^2}-\frac{1}{4^2)}}$$ = $$R_{H}$$ for the blue-green spectral line = 1.0972808+/-.000158005$$*10^{7}m^{-1}$$
 * $$\frac{(\frac{1}{434.05nm})}{(\frac{1}{2^2}-\frac{1}{5^2)}}$$ = $$R_{H}$$ for the violet spectral line = 1.0979866+/-.0001769$$*10^{7}m^{-1}$$

Rydberg Constant for Deuterium($$R_{D}$$)

 * $$\frac{(\frac{1}{660.6nm})}{1(\frac{1}{2^2}-\frac{1}{3^2})}$$ = $$R_{D}$$ for the red spectral line = 1.0899183+/-.00507$$*10^{7}m^{-1}$$
 * $$\frac{(\frac{1}{585.45nm})}{1(\frac{1}{2^2}-\frac{1}{4^2})}$$ = $$R_{D}$$ for the blue-green spectral line = 0.910980157+/-.00028$$*10^{7}m^{-1}$$
 * $$\frac{(\frac{1}{660.6nm})}{1(\frac{1}{2^2}-\frac{1}{5^2})}$$ = $$R_{D}$$ for the violet spectral line = 1.09645516$$*10^{7}m^{-1}$$(no +/- due to only seeing the two spectral lines and having only one data point)

Accepted Rydberg constant
The accepted value for the Rydberg constant is $$R_{actual}=1.09677\times 10^7m^{-1}$$.

My values are for Hydrogen:

$$R_{3\rightarrow 2}=1.0944245\times 10^7\times m^{-1}$$ which is off by 0.204%

$$R_{4\rightarrow 2}=1.097281\times 10^7\times m^{-1}$$ which is off by 0.0557%

$$R_{5\rightarrow 2}=1.097987\times 10^7\times m^{-1}$$ which is off by 0.12%

So in all not too bad in the percentage off from the actual value.

$$R_{av}=1.09656147\times 10^7\times m^{-1}$$ which is off by .00965%

My values for Deuterium:

$$R_{3\rightarrow 2}=1.0899183\times 10^7\times m^{-1}$$ which is off by 0.617%

$$R_{4\rightarrow 2}=0.91098\times 10^7\times m^{-1}$$ which is off by 16.9%

$$R_{5\rightarrow 2}=1.09645516\times 10^7\times m^{-1}$$ which is off by 0.0196%

So not as good as the Hydrogen this is due to the difference in the values from day 1 and day 2. The data is so off its inconclusive and I cannot see what difference that it makes to have a heaver nucleus.

Errors

 * Errors can be made in adjusting the width of the slit in that the intensity of the light coming through is diminished and that may cause problems when trying to identify spectral lines that might not be that intense and could be missed.
 * More errors can come from the gear back lash in terms of how the gears don't completely mesh up when adjusting the screw in opposite directions so you need to take that into account when adjusting the screw.
 * I believe that we looked at different orange lines from day one to day two so that's why the values are off for the orange lines on hydrogen from day one compared to day two.
 * Another error from day one compared to day two is that we could not see all the same spectral lines in Deuterium that we saw on day 1 compared to those we say on day two. We seemed to lose 3 of the spectral lines I don't know why, but it happened that way.
 * Systematic Errors could occur when we were taking measurements on the dial due to the potential slipping of the gears in the screw adjustment.  Another source of systemic errors could come from the dial and the difficulty in reading it being that you had do approximate the decimal positions for the wavelength.

=References= Phyc 307L page Blamer Notes

Dr Golds Lab Manual

David's Home

David's Notebook

Wiki Article on Hydrogen Spectral Lines

Wiki Article on Blamer Series