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Rutherford scattering

Inside the Nucleus

Wave or Particle?

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Rutherford's Notebook

Wave or Particle?

In the 1950s, experimenters began to use higher energy particles, from particle accelerators, which allowed them to examine the nucleus in greater detail.  This is because a particle with a higher energy has a shorter wavelength and a short wavelength can pick up more detail than a longer wavelength.  In fact, it is the momentum of the particle that is directly related to the wavelength, as Louis de Broglie proposed in his PhD thesis in 1924.  The de Broglie relation states that momentum, p, and wavelength, l, are related by:

p=h/l

where h is Planck's constant.

Rutherford and Chadwick had discovered the constituents of the nucleus by knocking protons and neutrons out of the nuclei.  The experiments in the 1950s, by contrast, in effect shone a beam of electrons into a nucleus, and revealed the contents by the scattering of the beam.

Probing the nucleus: Electrons with a wavelength similar to the radius of a nucleus first became available in 1953, at an accelerator at the Stanford University, used by Robert Hofstadter and colleagues. Hofstadter's experiments with nuclei such as gold and carbon showed clear differences from scattering from a point charge, as expected.  However, when targets of high pressure hydrogen gas became available in 1954, he could study scattering from single protons (hydrogen nuclei) and found that the proton also was not a point object, but had a size that was "surprisingly large", about 0.75 x 10-13cm. Later, he found that higher energy electrons would scatter from the protons within a larger nucleus - the electrons could "see" inside the nucleus.

The graph on the left shows Hofstadter's results for the amount of scattering (cross section) at different angles, compared with scattering from a point charge ("Mott curve") and for a more sophisticated calculation ("anomalous moment curve") that includes effects due to the proton's intrinsic spin (see here for more about spin).  The "experimental curve" through the data points allows for the proton's size, and gives the result of 0.7 x 10-13cm.

 




When Hofstadter later used higher energy electrons, he found they could "see" the protons inside nuclei.  The diagram below shows the number of electrons scattered at 45
° with different energies from hydrogen and helium nuclei.  In the case of hydrogen, the electrons scatter from single protons as in a billiard ball collision (elastic scattering), and give a peak at a specific energy of about 360 MeV (the initial energy of the electrons was 400 MeV).  The results for helium also show a peak - this time at about 385 MeV - but in this case there is an additional bump around 340 MeV.  The peak corresponds to elastic scattering of the electron from the helium nucleus, while the bump is elastic scattering from the two protons inside the helium nucleus.  This is why it is around the energy of the hydrogen peak.  It is smeared out because the protons are moving around inside the helium nucleus, so they have a range of kinetic energies when the electrons scatter from them.

protgraph.GIF (31441 bytes)

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