Read the following passage and answer the accompanying questions - Leaving Cert Physics - Question (a) - 2021

The forces experienced by a proton, in decreasing order of strength, are:

1. Strong nuclear force
2. Electromagnetic force
3. Weak nuclear force
4. Gravitational force

The Planck constant has a value of:

$6.6 imes 10^{-34} ext{ J s}$

To express this in terms of metres, kilograms, and seconds, we note that:

1 Joule (J) = 1 kg m² s⁻², hence:

$6.6 imes 10^{-34} ext{ J s} = 6.6 imes 10^{-34} ext{ kg m}^2 ext{s}^{-1}$

The nuclear equation for the pair annihilation of a proton (p) and an antiproton (p̄) is:

Using the equation for energy-mass equivalence:

$E = mc^2$

The mass of a muon (μ) is approximately:

$m ext{ (muon)} imes 2 = 2 imes 206 ext{ MeV/c}^2 \ = 3.769 × 10^{-28} ext{ kg}$

The energy of the photon is:

$E = (3.769 imes 10^{-28} ext{ kg}) imes (3 imes 10^8 ext{ m/s})^2 = 3.215 × 10^{-11} ext{ J}$

To convert this to electronvolts (eV), use:

$1 ext{ eV} = 1.6 imes 10^{-19} ext{ J}$

Thus:

$E = \frac{3.215 × 10^{-11} ext{ J}}{1.6 × 10^{-19} ext{ J/eV}} \\ = 2.01 × 10^{8} ext{ eV}$

(a) Particles in the Large Hadron Collider are accelerated using electric fields in the form of radiofrequency cavities, which increase the energy of the particles as they pass through.

(b) Particles are maintained in circular motion using magnetic fields generated by bending magnets, which keep the particles on a curved path.

1. The first experimental verification of $E = mc^2$, confirming the fundamental relationship between mass and energy.

2. The transmutation using artificially accelerated particles which advanced the field of nuclear physics and contributed to our understanding of particle interactions.