Fine Structure of Sodium

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Fine Structure of Sodium

• Presenter Alex Mott
• Lab Partner Diana Walling
• MIT Junior Lab
• Fall 2006

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Overview

• Fine Structure Corrections to the simple model
  of the atom
• Relativistic Corrections
• Spin-Orbit Coupling
• Electron Screening
• Experimental Setup
• Sodium Spectrum
• Doublet values and doublet energy separation
• Energy Diagram for Sodium
• Conclusions

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Motivation

• Precise knowledge of sodium spectrum
• Astrophysics - redshift
• Spectroscopy
• Validates QM description of the atom

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Relativistic Correction

• For any system
• Non-relativistic approximation
• Relativistic form
• Relativistic correction
• On the order

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Spin-Orbit Coupling

• Magnetic field due to proton
• Does not commute with
• Total angular momentum
• Energy dependent on electron spin

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Fine Structure Correction

• Both corrections on order
• For hydrogen the exact result is
• In general
• Electron-Electron repulsion

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Electron Screening
Radial Wavefunctions for Hydrogen
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Experimental Setup
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Observed Doublets
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3p and 4p Energy Separation
Energy Separation of 3p level
Energy Separation of 4p level
Ratios
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Approaches Degeneracy when n is large l is large
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Error Analysis

• Calibration Error 0.05 A
• Step Size 0.1 A
• Other elements in lamp
• Hydrogen
• Ambient Light
• Errors are small overall

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Conclusions

• We have seen fine structure effects emerge
• Results agree with the 3p and 4p doublet
• Results consistent with
• Energy Spectrum is non-degenerate
• Need more data to find exact relationship

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