Wave or Particle?
If you want to know more
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:
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.