FranckHertz Experiment

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Franck-Hertz Experiment

• T.J. Torres

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Outline

• Motivation and Theory
• Experimental Setup and Concerns
• Data and Analysis
• Error Propagation
• Results and Conclusion

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Motivation and Purpose

• Line spectra of elements gives quantized energy
  spectrum for electronic transitions in atom.
• Does collision behavior reflect evidence of
  discreet energy spectra?
• Wish to look at electron collisions with atomic
  gas.
• Want to show discreet energy absorption from
  inelastic electron collisions with Mercury vapor.

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Theory

• Energy spectrum from thermionic emission is
  Maxwell-Boltzmann, and given by
• Where A is a normalization constant given by
  via Richardsons
• equation.
• Emission for atomic gasses correspond to change
  in energy of transition by

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Experimental Setup

• Electrons from filament accelerated toward grid.
• Retarding potential from grid to cathode.
• Hg vaporized using oven controlled by variac.
• Current monitored using Keithly multimeter.

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Concerns

• Oven temperature set so that mean free path is
  short in comparison with distance from grid to
  cathode (145 degrees C).
• Filament voltage set to give tube current in nA
  range (4.28 V).
• Set accelerating voltage to overcome space charge
  limited current.
• Retarding voltage set to discriminate for first
  excitation potential (1.76 V).
• Dual low-pass filters from output signals to
  reduce noise.

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Franck-Hertz Data

• Direct data from oscilloscope x-y view screenshot.

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Corrected by contact potential value to
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Error Propagation

• Initial error in intervals was
• determined by taking into account noise from
  the output of the multimeter into the
  oscilloscope.
• Weighted mean found from taking
• Error is then given as
• Error for sum and differences calculated using
  sum of squares with 0 covariance.

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Possible Causes of Error

• Noise from signal (tried to minimize with
  low-pass filter).
• Energy distribution from thermionic emission
  induces statistical errors.
• Pressure gradient in tube due to uneven heating.
• Varying electron acceleration distances due to
  varying free path.

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Results

• Recall that . We can then
  compare this to the expected value of 4.86eV for
  the energy difference between Hg ground state
  and first excited state.
• The minima show that energy can only be absorbed
  from electron collisions in discreet packets.
• Ionization potential of Mercury found to be