User:David K. O'Hara/Notebook/physics 307 lab/balmer series
Lab Balmer Series
^{SJK 21:36, 14 November 2009 (EST)}Contents
Theory
Lab Objectives
In this lab we will calibrate an optical spectrometer using the known mercury spectrum.
Study the Balmer Series in Hydrogen spectrum.
Determine the Rydberg Constant for Hydrogen.
Last, compare Hydrogen with Dueterium.
Using a constant deviation spectrometer, which has the characteristic that the angle of incidence and the angle of exit are the same for all wavelengths when the prism is properly oriented. All that is required for the spectral analysis of light is to rotate the prism relative to the incident light keeping the incident ray and the axis of the analyzing telescope fixed at 90 degrees. The rotation of the prism is calibrated with a known source (mercury in this case), and an interpolation of the known lines is used for the final calibration. See this link about constant deviation prisms [Pellin-Broca Prisms].
Equipment
- Adam Hilger London Spectrometer. Serial Number 12610
- Spectrum Tube Power Supply Model SP200 5000V 10 mAmps electro technic products
- Spectrum Tube, Mercury Vapor S-68755-30-K
- Spectrum Tube, Hydrogen S-68755-30-G
- Spectrum Tube, Deuteruim S-68755-30-E
- Spectrum Tube, Krypton S-68755-30-?
Safety
Cautions for electric shock due to the high voltage (5000v)the power supply runs across the sample tubes to make them light up.
Spectrometer is very old and not built to stand up to rough handling.
Sample tubes are glass and need careful handling to prevent breaking.
One of the samples is mercury which is toxic if released out of the tube and would be quite hazardous to anyone in the vicinity. Any lack of containment would require containment and proper clean-up/disposal immediately.
Lastly, the sample tubes do get quite hot as they are lit for periods of time. You have to let them cool before you can safely change from one tube to another.
Procedure
Using the spectrometer shown on the right:
First step is to calibrate the spectrometer using the mercury lamp.
1. Power up the mercury tube and let it warm up for about 5 minutes 2. With the spectrometer slit wide(.5-1mm) find a line of the Hg spectrum. 3. Narrow the slit until the mercury line becomes sharp and narrow. 4. Locate all mercury lines possible.
wavelength (nm) | color | measured λ | measured λ (2nd run) | measured λ (3rd run) | |
---|---|---|---|---|---|
404.7 | deep violet | 404.7 | 404.9 | not visible | |
435.8 | violet | 434.2 | 435.5 | 435.7 | 436.2 |
skip | blue-green | 488.8 | 490.9 | 491.1 | 491 |
546.1 | green | 541.1 | 545 | 547 | 546.2 |
577.0 | yellow | 574.5 | 578 | 578.5 | 577.8 |
579.0 | yellow | na | na | 581.3 | 579.5 |
690.75 | red | 695 | difficult to see | not visible | not visible |
First run on calibrating the prism, I left the slit wide to allow plenty of light through and measured from the center of each line. This particularly affected the reading on the yellow lines as the resolution was too poor to pick out both lines. For the second run I will reduce the slit width and take the readings from the leading edge of the observed lines.
Still had the slit too wide for the second run, yellow lines were still not defined as a duo and noticeable error propagation as it got to the end of the scale. Did seem better lined up than the first set though. But I should have realized that if I could pick a leading edge of the lines, then the lines were too fat. Hopefully the third time is the charm.
For the third run, I have made sure I have the duo of yellow lines, I set the measurement for 546.1nm and then I centered the green line on the crosshairs. Data were taken from 400nm up.
The Fourth run I left everything the same but worked from 700nm down. Made sure to use the same eye (left) for each measurement and tried to reduce all sources of parallax that I could(viewing angle, head pitch, etc.). Seemed to be the truest set of data I took for the mercury lamp.
data
Getting the Hydrogen lamp, I decided to pass on the one with "blown" written on a piece of paper taped to sample and went with another Hydrogen tube. Again, measurements were taken from 700 nm down.
Take hydrogen Data, should see 4-5 lines, record raw and corrected data.
color | Raw measured λ run1 | Raw measured λ run2 | λ correction |
---|---|---|---|
red | 657.2 | 657 | |
blue-green | 485.8 | 486 | |
blue-violet | 434 | 433.7 | |
deep violet | 410 | 410.1 |
Accepted wavelengths of these lines pulled from this wikipedia page for [balmer series]
Red 656.3 nm
Blue-Green 486.1 nm
Blue 434.1 nm
Violet 410.2 nm
day 2 measurements
to begin day 2 I started again with calibrating the spectrometer using the mercury lamp. I took the measurement for the green line multiple times to find an error range for that measurement, then I applied that error range to the rest of the lines to make sure all the data I would take would be within that range.
^{SJK 20:40, 14 November 2009 (EST)}λ expected(nm) | 546.1 line(nm) | 546.1 line(nm) | 546.1 line(nm) | 546.1 line(nm) | error range (nm) | λ measured (nm) |
---|---|---|---|---|---|---|
579.0 (yellow) | 579.2 | |||||
577.0 (yellow) | 576.8 | |||||
546.1 (green) | 546.0 | 546.3 | 546.5 | 545.8 | =+/-.25 | 545.9 |
435.8 (violet) | 435.6 |
all the data for the mercury lines is within my error expectation predicted off of the green line measurements.
2nd day hydrogen data set 1 (run 3)
λ measured (nm) w/error margin |
---|
656.1 +/-0.25 (red) |
485.9 +/-0.25 (cyan) |
434.2 +/-0.25 (blue-violet) |
410.2 +/-0.25 (faint violet) |
2nd day Hydrogen data set 2(4th run)
λ measured (nm) w/error margin |
---|
656.1 +/-0.25 (red) |
486.0 +/-0.25 (cyan) |
434.3 +/-0.25 (blue-violet) |
410.3 +/-0.25 (faint violet) |
Dueterium Data
λ measured (nm) w/error margin |
---|
656.0 +/-0.25 (red) |
485.3 +/-0.25 (cyan) |
433.9 +/-0.25 (blue-violet) |
409.2 +/-0.25 (faint violet) |
Dueterium 2nd Run
λ measured (nm) w/error margin |
---|
655.9 +/-0.25 (red) |
485.3 +/-0.25 (cyan) |
434.1 +/-0.25 (blue-violet) |
409.6 +/-0.25 (faint violet) |
Dueterium 3rd run
λ measured (nm) w/error margin |
---|
655.8 +/-0.25 (red) |
485.4 +/-0.25 (cyan) |
433.9 +/-0.25 (blue-violet) |
409.7 +/-0.25 (faint violet) |
Dueterium 4th run
λ measured (nm) w/error margin |
---|
656.0 +/-0.25 (red) |
485.5 +/-0.25 (cyan) |
433.8 +/-0.25 (blue-violet) |
409.6 +/-0.25 (faint violet) |
Krypton
The Lab manual also suggests reading the spectrum from a Sodium Lamp which was not available so I substituted Krypton instead of Na. krypton first run
λ measured (nm) w/error margin |
---|
586.9 +/-0.25 (orange) |
556.5 +/-0.25 (green) |
431.5 +/-0.25 (violet) |
426.8 +/-0.25 (violet) |
krypton second run
λ measured (nm) w/error margin |
---|
586.8 +/-0.25 (orange) |
556.3 +/-0.25 (green) |
431.3 +/-0.25 (blue-violet) |
426.8 +/-0.25 (faint violet) |
Since the point of the exercise was to see if you could resolve the two sodium lines which are very close together, this part of the lab while interesting to see the characteristic orange and green krypton lines, was quite pointless.
Analysis
The value for the Rydberg constant is given by the equation:
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle \frac{1}{\lambda }=R_{H}(\frac{1}{2^{2}}-\frac{1}{n^{2}})}
With the accepted value for that constant as R_{h}=1.097272 x 10^{7}m^{-1} [|Ryderg constant wiki page]
To find the value of n for the wavelengths measured I again used this page as a resource [|balmer equation]
This spreadsheet shows values for the Hydrogen and Deuterium lines average wavelength and the standard error of the mean for the measurements
File:Balmer data.xlsx
using this equation to find R_{H}
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle \frac{\frac{1}{\lambda }}{(\frac{1}{2^2}-\frac{1}{n^2})}=R_{H}}
- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle \frac{(\frac{1}{656.6nm})}{(\frac{1}{2^2}-\frac{1}{3^2)}}} = Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle R_{H}} for the red spectral line = 1.0965580Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle *10^{7}m^{-1}}
- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle \frac{(\frac{1}{485.925nm})}{(\frac{1}{2^2}-\frac{1}{4^2)}}} = Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle R_{H}} for the cyan spectral line = 1.0953089Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle *10^{7}m^{-1}}
- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle \frac{(\frac{1}{434.05nm})}{(\frac{1}{2^2}-\frac{1}{5^2)}}} = Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle R_{H}} for the blue-violet spectral line = 1.0970866Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle *10^{7}m^{-1}}
- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle \frac{(\frac{1}{410.15})}{(\frac{1}{2^2}-\frac{1}{6^2)}}} = Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle R_{H}} for the violet spectral line = 1.0971595Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle *10^{7}m^{-1}}
The Rydberg constant that i calculated for hydrogen from my data was 1.0965283e7 m-1 +/-4300
Dueterium data
- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle \frac{(\frac{1}{655.925nm})}{(\frac{1}{2^2}-\frac{1}{3^2)}}} = Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle R_{D}} for the red spectral line = 1.0976864Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle *10^{7}m^{-1}}
- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle \frac{(\frac{1}{485.375nm})}{(\frac{1}{2^2}-\frac{1}{4^2)}}} = Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle R_{D}} for the cyan spectral line = 1.0988067Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle *10^{7}m^{-1}}
- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle \frac{(\frac{1}{433.925nm})}{(\frac{1}{2^2}-\frac{1}{5^2)}}} = Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle R_{D}} for the blue-violet spectral line = 1.0974027Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle *10^{7}m^{-1}}
- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle \frac{(\frac{1}{409.525})}{(\frac{1}{2^2}-\frac{1}{6^2)}}} = Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle R_{D}} for the violet spectral line = 1.0966340Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle *10^{7}m^{-1}}
The Rydberg constant that i calculated using my dueterium data was 1.0976325e7 m-1 +/-4500, slightly different from hydrogen due to the heavier atom.
- Equation formatting taken from David Weiss openwetware page "balmer lab notes"
Conclusions
The value of the Rydberg constant I calculated for hydrogen was 1.0965283e7 m-1 +/-4300. This compared to the accepted value of the Rydberg Constant of 1.097272 x 107 m-1.
^{SJK 21:35, 14 November 2009 (EST)}This gives a percent error from the accepted value of .000678 which is the closest I have come to an accepted value in this class.
Possible sources of error: The scale on the spectrometer is not fine enough to be accurate to a tenth of a nanometer so all measurements are off by as much as a quarter nm. The way you set up to view the spectral lines in the scope has a susceptibility to induce a large amount of parallax, especially dealing with such fine measurements. As stated in the lab manual, the tradeoff between resolution vs brightness puts the experimenter in the position of trying to find the optimal condition for viewing the spectral lines.