RUTHERFORD SCATTERING

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RUTHERFORD SCATTERING

• T.J. Torres

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OUTLINE

• Introduction
• Motivation
• Rutherford versus Plum-pudding Model
• Experiment and Setup
• Alpha Beam Characteristics
• Data and Analysis
• Error Analysis
• Results and Conclusion

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INTRODUCTION

• There was much confusion amongst physicists about
  the structure of the atom during the early
  twentieth century.
• Plum-pudding model proposed in1897 after electron
  discovery.
• Experimental evidence in 1909 conflicted with the
  Plum-pudding model.
• Ernest Rutherford predicts different atomic
  structure with a massive center of positive
  charge.
• The two models are conflicting.

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MOTIVATION

• Experimental Purpose
• To compare results from alpha particle scattering
  off Au foil to the predicted theoretical results
  from both the Rutherford and Plum-pudding models
  of the atom.
• Importance
• If the comparison of our data to one of the
  models is strong enough, we can make with
  reasonable certainty claims about how the atom is
  structured, advancing human understanding of
  matter and the world around us.

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RUTHERFORD AND PLUM-PUDDING MODELS OF THE ATOM

• Plum-pudding

• Rutherford

• Electrons were free to move in a cloud of
  positive charge.
• Little explanation about atomic mass.
• Allowed for electron movement and bound states.

• Electrons reside outside a heavy center of
  positive charge.
• Mass of atom resides predominantly within the
  nucleus.
• Allowed for electron movement in orbits, but gave
  no structure to bound states.

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RUTHERFORD AND PLUM-PUDDING MODELS OF THE ATOM
(THEORETICAL PREDICTIONS)

• Plum-pudding

• Rutherford

• Fractional Scattering Distribution
• Where is the mean multiple scattering
  which we shall take to be 1 degree.

• Fractional Scattering Distribution

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EXPERIMENT

• Alpha particle howitzer fixed to Au foil.
• Both are rotated relative to the detector, and
  counting results are recorded on MCA.
• Apparatus contained in vacuum to reduce energy
  loss from air

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ALPHA BEAM CHARACTERISTICS
Beam width and maximum obtained by taking count
measurements at 10 degrees to either direction of
proposed center.
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DATA (PLUM PUDDING FITTING)

• Deviance at even 10 degrees outside the beam
  center is far too large to obtain a reasonable
  fitting with Matlab. Thus under the most generous
  circumstances there model does not agree with our
  data.

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DATA (RUTHERFORD FITTING)

• Data presents good correlation with the
  Rutherford model and all residuals are reasonably
  close to the fit line with the exception of one
  point which can be attributed to error.

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COMPARISON TO THEORETICAL RESULT

• Recall that
• We use the same functional model for fitting, so
  we need only compare the theoretical and
  experimental values of multiplied by the
  initial count rate.

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ERROR ANALYSIS

• Possible Contributors to error
• Noticed oddly shaped pulses during certain data
  gathering periods that suggest false count number
  due to loose wiring.
• Run time allotment only allowed for limited
  statistical accuracy.
• Multiple Scattering.
• Foil thickness error due to incomplete vacuum.
• Noise from improper detector bias/discriminator
  settings

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RESULTS AND CONCLUSIONS

• Recall that for the Plum-Pudding model our data
  had a correlation .
• Similarly, for the Rutherford model
• We conclude from this with reasonable certainty
  that our data agrees strongly with the Rutherford
  model and not at all for the angles of interest
  with the Plum-pudding model.
• The agreement between experimental and
  theoretical calculation had an error of around
  44, which suggests that the model still holds
  true for the atom if allowances for error are
  taken into account.
• One concludes that the atom is comprised of a
  massive nucleus with positive charge.