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 shorter 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.

Fermi proposed the equation for the radius of a
nucleus (r) in terms of the radius of the hydrogen nucleus (r_{o}) and the nucleon
number of the nucleus (A)

The constant r

Calculate the radii of the following nuclei:

(a) carbon 12 (A = 12)

(b) gold 197 (A = 197)

(a) r = 10

(b) r = 10

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 (Stanford
Linear Accelerator Centre) 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 3x108]/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.