The new Swiss 200-franc note honours proton-proton collisions in the Large Hadron Collider (LHC) at CERN - Leaving Cert Physics - Question d (i) - 2019

The conservation of charge principle states that the total electric charge before and after a collision must be the same. Since two protons (each positively charged) collide, their total charge is +2. The creation of one neutral pion ($ext{π}^0$) keeps the total charge conserved, as the other protons remain, leaving the overall charge at +1.

The total kinetic energy (E) can be calculated using the equation:

$E = \frac{1}{2} mv^2$

For two protons:

• For a single proton:

$E_{b} = \frac{1}{2} (1.6726 \times 10^{-27} kg) (0.9 \cdot (2.9979 \times 10^{8} m/s))^2$

Calculate:

• $E_{b} = 1.2176 \times 10^{-10} J$

Total kinetic energy of all three particles can then be calculated as:
$E = mc^2 / E_a = E_b - m_ec^2$

This leads to: $E_a = 1.00 \times 10^{-10} J$

The protons are maintained in circular motion by magnetic fields which provide the necessary centripetal force. As protons move through the circular accelerator, magnetic fields act perpendicular to their direction of motion, continuously altering their path and keeping them in a circular trajectory.

The principal advantage of a circular accelerator is that a greater energy can be created. This occurs because particles can gain energy through multiple circuits around the accelerator, effectively allowing for longer paths and more interactions.