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

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

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?

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

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

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

Experimental setup parameters Slit sizes: quality of lineshape vs.

signal size Integration time: -error vs.

patience

N

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

Typical monochromator data

Voigt gives better fit than Gaussian, but the means agree! Typical errors in fitted mean: ~0.001 A

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

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

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

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

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

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