tony hyun kim (partner: connor mcentee) 12/8/2008 8.13 mw2-5 prof. roland
DESCRIPTION
Tony Hyun Kim (Partner: Connor McEntee) 12/8/2008 8.13 MW2-5 Prof. Roland. Optical Spectroscopy of Hydrogenic Atoms: Rydberg fits of 1 H and 2 H, and Determination of the mass ratio. Topics to be discussed. Introduction Historical context Quantum mechanics of atomic emission - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: Tony Hyun Kim (Partner: Connor McEntee) 12/8/2008 8.13 MW2-5 Prof. Roland](https://reader036.vdocument.in/reader036/viewer/2022062310/568162a0550346895dd3183b/html5/thumbnails/1.jpg)
Optical Spectroscopy of Hydrogenic Atoms:Rydberg fits of 1H and 2H, and Determination of the mass ratio
Tony Hyun Kim(Partner: Connor McEntee)12/8/20088.13 MW2-5 Prof. Roland
![Page 2: Tony Hyun Kim (Partner: Connor McEntee) 12/8/2008 8.13 MW2-5 Prof. Roland](https://reader036.vdocument.in/reader036/viewer/2022062310/568162a0550346895dd3183b/html5/thumbnails/2.jpg)
Topics to be discussed
1. Introduction1. Historical context2. Quantum mechanics of atomic emission
2. Experimental setup3. Analysis and Results
1. Fitting the lineshape2. Mercury calibration3. Hydrogen and deuterium fits
4. Sources of Error; Possible improvements5. Conclusions
1. Verification of the hydrogen Rydberg2. Estimate of the hydrogen-deuterium mass ratio
![Page 3: Tony Hyun Kim (Partner: Connor McEntee) 12/8/2008 8.13 MW2-5 Prof. Roland](https://reader036.vdocument.in/reader036/viewer/2022062310/568162a0550346895dd3183b/html5/thumbnails/3.jpg)
Image source: http://en.wikipedia.org/wiki/Emission_spectrum
Atomic spectra: a historical context
By 19th century, tremendous amounts of atomic spectral data collected.
What are the underlying mathematical patterns and the physical explanations?
![Page 4: Tony Hyun Kim (Partner: Connor McEntee) 12/8/2008 8.13 MW2-5 Prof. Roland](https://reader036.vdocument.in/reader036/viewer/2022062310/568162a0550346895dd3183b/html5/thumbnails/4.jpg)
Image source: http://en.wikipedia.org/wiki/Emission_spectrum
Atomic spectra: a historical context
By 19th century, tremendous amounts of atomic spectral data collected.
What are the underlying mathematical patterns and the physical explanations?
22
111
fi nnR
![Page 5: Tony Hyun Kim (Partner: Connor McEntee) 12/8/2008 8.13 MW2-5 Prof. Roland](https://reader036.vdocument.in/reader036/viewer/2022062310/568162a0550346895dd3183b/html5/thumbnails/5.jpg)
Image source: Griffiths. "Intro. to QM (2nd Ed.)" Pearson 2005.
QM of the optical electron Reduced, one-body SE yields
eigenenergies:
Light emitted when electron undergoes transition: ni nf
2
2
0
2
2
142 neEn
22
2
0
2
3
1144
1
if nne
c
2
0
2
3 44
ec
R
hchE
![Page 6: Tony Hyun Kim (Partner: Connor McEntee) 12/8/2008 8.13 MW2-5 Prof. Roland](https://reader036.vdocument.in/reader036/viewer/2022062310/568162a0550346895dd3183b/html5/thumbnails/6.jpg)
Image source: http://en.wikipedia.org/wiki/Monochromator
Experimental setup: Basic principles
Used JY1250M monochromator (R ~ 104 0.03 A step size!) Counter indicates the orientation of grating
![Page 7: Tony Hyun Kim (Partner: Connor McEntee) 12/8/2008 8.13 MW2-5 Prof. Roland](https://reader036.vdocument.in/reader036/viewer/2022062310/568162a0550346895dd3183b/html5/thumbnails/7.jpg)
Experimental setup parameters Slit sizes: quality of lineshape vs.
signal size Integration time: -error vs.
patience
N
![Page 8: Tony Hyun Kim (Partner: Connor McEntee) 12/8/2008 8.13 MW2-5 Prof. Roland](https://reader036.vdocument.in/reader036/viewer/2022062310/568162a0550346895dd3183b/html5/thumbnails/8.jpg)
Experimental setup parameters Slit sizes: quality of lineshape vs.
signal size Integration time: -error vs.
patience
Most important:
N
Shot-to-shot repeatability!0.17 A
![Page 9: Tony Hyun Kim (Partner: Connor McEntee) 12/8/2008 8.13 MW2-5 Prof. Roland](https://reader036.vdocument.in/reader036/viewer/2022062310/568162a0550346895dd3183b/html5/thumbnails/9.jpg)
Typical monochromator data
Voigt gives better fit than Gaussian, but the means agree! Typical errors in fitted mean: ~0.001 A
![Page 10: Tony Hyun Kim (Partner: Connor McEntee) 12/8/2008 8.13 MW2-5 Prof. Roland](https://reader036.vdocument.in/reader036/viewer/2022062310/568162a0550346895dd3183b/html5/thumbnails/10.jpg)
Mercury calibration Monochromator’s counter is not physically accurate
Produced quadratic conversion function:)4.23.79()001.0997.0(10)6.15.3( 27
CRCCRCMC
![Page 11: Tony Hyun Kim (Partner: Connor McEntee) 12/8/2008 8.13 MW2-5 Prof. Roland](https://reader036.vdocument.in/reader036/viewer/2022062310/568162a0550346895dd3183b/html5/thumbnails/11.jpg)
![Page 12: Tony Hyun Kim (Partner: Connor McEntee) 12/8/2008 8.13 MW2-5 Prof. Roland](https://reader036.vdocument.in/reader036/viewer/2022062310/568162a0550346895dd3183b/html5/thumbnails/12.jpg)
Results: Hydrogen Rydberg Our measured value:
Correct for index of refraction of air (n = 1.0003)
Compare to published value: 17
, 10096776.1 mR NISTH
17, 10)00002.009678.1(/ mnR EXPTH
17, 10)00002.009711.1( mR EXPTH
![Page 13: Tony Hyun Kim (Partner: Connor McEntee) 12/8/2008 8.13 MW2-5 Prof. Roland](https://reader036.vdocument.in/reader036/viewer/2022062310/568162a0550346895dd3183b/html5/thumbnails/13.jpg)
Results: 1H/2H mass ratio From …
Compute mD using known values of me, mp (NIST)
Published value:
DHDH RR //
17.087.1
EXPTH
D
mm
999.1
NISTH
D
mm
![Page 14: Tony Hyun Kim (Partner: Connor McEntee) 12/8/2008 8.13 MW2-5 Prof. Roland](https://reader036.vdocument.in/reader036/viewer/2022062310/568162a0550346895dd3183b/html5/thumbnails/14.jpg)
An improved optical setup Since we regard the Hg-lines as “ruler”… Scheme for circumventing the 0.17A mechanical error:
Especially useful for isotope shift measurement
Superimpose sources
MonochromatorInput
![Page 15: Tony Hyun Kim (Partner: Connor McEntee) 12/8/2008 8.13 MW2-5 Prof. Roland](https://reader036.vdocument.in/reader036/viewer/2022062310/568162a0550346895dd3183b/html5/thumbnails/15.jpg)
Conclusions Performed spectroscopy of 1H/2H
The Rydberg formula for hydrogen was confirmed. Excellent agreement with published values:
Ratio of Rydberg constants was used to deduce mass ratio: 17.087.1
EXPTH
D
mm 999.1
NISTH
D
mm
17, 10)00002.009678.1( mR EXPTH
17, 10096776.1 mR NISTH
![Page 16: Tony Hyun Kim (Partner: Connor McEntee) 12/8/2008 8.13 MW2-5 Prof. Roland](https://reader036.vdocument.in/reader036/viewer/2022062310/568162a0550346895dd3183b/html5/thumbnails/16.jpg)
![Page 17: Tony Hyun Kim (Partner: Connor McEntee) 12/8/2008 8.13 MW2-5 Prof. Roland](https://reader036.vdocument.in/reader036/viewer/2022062310/568162a0550346895dd3183b/html5/thumbnails/17.jpg)
Large relative error on mass ratio? Recall:
Since nuclear mass has a subdued effect on overall reduced mass.
Hence, can expect large relative errors in nuclear mass, associated with minute errors in R.
ne mmR1111
en mm