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

In proton-proton collisions, charge conservation must be maintained. Each proton has a positive charge, contributing a total charge of +2. To balance this, the neutral pion ($ext{π}^0$) produced carries no charge, ensuring that the total charge after the collision remains at zero.

To calculate the total kinetic energy (TKE) of the three particles, we can use the formula:

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

For the protons:

• Protons have a rest mass of approximately $1.67 \times 10^{-27} kg$ and a velocity of $0.9c$ (where $c = 3 \times 10^8 m/s$).
• The total energy for each proton will include both its rest mass and kinetic energy components. We would also need to consider the mass of the neutral pion, which is about $1.67 \times 10^{-27} kg$ as well.

The calculations will detail the energy contributions from each component to arrive at the total kinetic energy after collision.

The protons in the Large Hadron Collider are maintained in circular motion by the application of magnetic fields. These magnetic fields provide the necessary centripetal force to keep the protons on their circular paths, ensuring they complete their orbits around the collider ring.

The principal advantage of a circular accelerator over a linear accelerator is that greater energy can be created. A circular design allows particles to gain energy as they loop through the accelerator multiple times, which leads to a longer path available for acceleration before they collide.