The scattering of high-energy
electrons by nucleons (protons and neutrons) can reveal the internal structure of these particles. It
was thought that nucleons were fundamental particles but the results of the electron scattering
experiments suggest the existence of point like particles within the proton.

At the
Stanford Linear Accelerator (SLAC) electrons are accelerated along the two mile
accelerator to an energy of 6 GeV (6 000 MeV or 6 000 000 000 eV). This is an energy of
1.6x10^{-19}x6x10^{9} J = 9.6x10^{-10} J.

What is the point of
this?

As you know the diffraction of particles depends on their wavelength and so
the more energetic the particle the shorted the wavelength and the finer the detail that can
be observed. So very high energies are needed to probe the very internal structure of a
proton or neutron.

From the Fermi equation (r = r_{o}A^{1/3}) we know that the "diameter" of a
nucleon is about 10^{-15} m and so if we want to have any chance of "seeing" inside a proton
we need to use something with a wavelength of this order or even smaller.

At the enormous energies produced by SLAC the electrons have a very short wavelength which
we can calculate using the de Broglie equation. Of course at such an energy the mass of
the electron will be greater than that of the electron at rest and this can be calculated using
the special relativity equations.

The rest mass of the electron = 9.1x10^{-31}
kg and so using classical mechanics and ignoring relativity for the moment:

The electron energy = eV = ½ mv^{2}

So 1.6x10^{-19} x 6x10^{9} = ½ x 9x10^{-31} x
v^{2} and so v = 4.6x10^{10} ms^{-1}, clearly impossible since it is greater than the
speed of light.

Using the mass-energy equation: E = mc^{2} to give mass (m) =
E/c^{2}, and that for momentum (p) = mv we have:

Momentum (p) = mv = [E/c^{2}]v
but at these enormous energies the velocity of the electron is close to that of light and so v =c.

Therefore: p = E/c

Then using the de Broglie equation we can find the wavelength of the
electron at this energy.

Electron wavelength(λ) = h/p = hc/E = [6.63x10^{-34} x
3x10^{8}]/9.6x10^{-10}= 2.1x10^{-16}
m

This wavelength is less than the "diameter" of a nucleon and so these very
high-energy electrons can be used to probe the "structure" of the proton or
neutron.

When these experiments were carried out it was found that the scattering
of electrons from a nucleon was not uniform as it would have been if nucleons were just a
single particle. Just like the alpha scattering from gold it showed evidence for smaller
particles within the nucleon – these were named **Quarks**.
(See: Quarks)