The Diameter of a Nucleon

• High energy electron beams can be used to analyse?nucleons, e.g.
  • Protons
  • Neutrons

• When electrons are accelerated to very high energies, they can?collide?with nucleon targets
• The?scattering pattern?is used to analyse the size and structure of nucleons
• To?resolve?detail, like the nucleon diameter, the?de Broglie wavelength?of the electron must be comparable to the?size of the nucleon
  • The de Broglie wavelength, and hence an approximation to nucleon diameter, is given by:

• Where:
  • λ?= de Broglie wavelength (m)
  • h?= Planck's constant (J s)
  • m?= mass (kg)
  • v?= velocity (m s–1)
• Note that electrons do not experience the?strong nuclear force
  • Therefore, they are able to get extremely close to the nucleons without interacting
  • This allows them to build up a better idea about the size of the nucleus than?alpha particles, which are comprised of protons and neutrons

Inside the Nucleon

• If electrons are accelerated to even?higher?energies, their de Broglie wavelength becomes even?smaller
  • This is because ?therefore the?faster?the electrons, the?smaller?their de Broglie wavelength

• Hence, the electron wavelength becomes small enough to be used to resolve?internal?structure of the nucleon
  • Such an electron beam would be able to resolve individual?quarks?inside the nucleon

Step 1: Refer to the de Broglie wavelength

• • The proton diameter ～ 10–15?m so the?de Broglie wavelength?of the electrons must be?at most?this size in order to resolve the internal structure of the proton

Step 2: Refer to the proportionality between wavelength and momentum

• • Since the de Broglie wavelength is?inversely proportional?to the momentum of the electrons, then they must be accelerated to very high velocity (and hence, energy) in order to obtain very short wavelengths