The Diameter of a Nucleon
- High energy electron beams can be used to analyse nucleons, e.g.
- 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:
≈ nucleon diameter
- 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
The diameter of a proton is of the order of 10–15 m.
Explain why electrons must be accelerated to very high energies if they are to be used to probe the internal structure of a proton.
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
Remember to use words like 'proportional' and 'inversely proportional' when explaining how two quantities relate to each other, using an equation.
In the case of particle physics, it is likely that you will be asked to explain effects based on the de Broglie wavelength λ, which you should remember is given by:
Therefore, the de Broglie wavelength λ is inversely proportional to particle momentum p and velocity v.