On October 15, 1991 a ultra-high energy proton came to earth, near Utah, from space with an energy of
$3.2\pm 0.9\times 10^{20}$ electron volts. This is REALLY a lot of energy for a proton to posess! To see why, explore the energy it contains by comparing this figure with the kinetic energy for the motion of more every-day objects. Find an everyday situation which really gives an intuitive sense of the amount of energy of this ultra-high energy proton.

Imagine that a small, hand-sized, ball of meteoric iron with the same kinetic energy per kilogram as this ultra-high energy proton struck earth. Analyse the possible effect this would have.

If you used the Newtonian expression $KE=\frac{1}{2}mv^2$ for the energy, how fast would the proton be travelling? How does this compare with the speed of light?

Extension: Clearly, the energies referred to in the question push the furthest reaches of Einstein's theory of special relativity. Use this situation to determine the actual velocity of the proton relative to Earth using the formula
$$E= \frac{m_0}{\sqrt{1-\frac{v^2}{c^2}}$$

The

Datea

1 electron volt = 1.60217646\times 10^{-19} joules
Rest mass of the proton is 938.28 MeV
Mass of proton 1.6726E-27kg

NOTES AND BACKGROUND

Cosmic rays are simply particles of matter moving through space; typically high energy protons, helium nuclei or electons. Modern models of physics currently under investigation by theoretical physicists predict bound on the energies of cosmic rays or the appearence of more exotic particles in cosmic rays.

Ultra-high energy particles are occasionally found in cosmic rays, confounding theoretical physicists and helping to drive forward the bounds of our understanding of the universe. An interesting article on the tounge-in-cheek 'Oh-my-god' particle, is found here .