The experiment for this is firing alpha particles with approximately 5MeV energy at a thin sheet of gold a few atoms thick. Most particles will travel straight through the sheet, but a small proportion will be deflected through large angles.
At greater velocities, the closer it can get to the gold nucleus and the less it will be deflected. This is because the faster it will be going, the less time it will spend at a certian distance so the less acceleration there will be.
The distance of closest approach can be calculated using the equation KE = kQq/r. This is because, at the closest that the alpha particle can get to the nucleus, the electric potential energy is equal to kinetic energy.
This proves that there is a positive, central nucleus which is significantly more massive than the alpha particle.
The limitation of this experiment is that the alpha particle is positive so cannot directly collide witht the nucleus.
Alpha scattering is an example of an elastic collision.
Low Energy Electron Scattering
The electrons are not repelled by the nucleus and are not affected by the strong force.
Most of the electrons will travel straight through the gold foil and some will be deflected, as with alpha scattering. However, due to the particle-wave model, electrons can also behave as waves. This means that the electrons are also diffracted. The greatest diffraction occurs when the wavelength of the electrons is close to the size of the nucleus.n
nλ = dsinθ for a maxima
λ/2 = dsinθ for a minima
This can allow us to calculate the diameter of the nucleus, and is elastic scattering.
The average energy for these electrons is 300MeV.
Due to the high energy of the electrons, the relativistic factor applies.
γ = Etotal/Erest
To find the radius of a nucleus, you can use the formula r = r(o)A^1/3
Where r(o) is the radius of a single nuclei, a constant.
High Energy Electron Scattering
This is deep inelastic scattering, and the electrons have energies around 1 GeV.
The electron enters either a proton or neutron and interacts with a quark. This involves the exchange of high energy electrons, which leads to pair production. This allows mesons to be ejected from the nucleus as they are particle-antiparticle pairs.
This type of scattering can be used to show the distribution of charge within a nucleus.