10. Answer either part (a) or part (b) - Leaving Cert Physics - Question 10 - 2012

The equation representing this interaction is:

$e^- + e^+ \rightarrow \gamma + \gamma$

This denotes the annihilation of the positron and electron, resulting in the production of two photons.

Photons are produced as a result of the annihilation of the positron and electron, which converts their mass into energy, according to Einstein's mass-energy equivalence principle (E=mc²). This process conserves energy and momentum.

To calculate the minimum frequency ($f$) of the produced photons, first, determine the energy equivalent of the combined mass of the positron and electron:

$E = (m_{e^-} + m_{e^+}) c^2$

where the mass of the electron ( extit{m}) is approximately $9.10938356 imes 10^{-31}$ kg.

Thus, the total mass is:

$m_{total} = 2 \times 9.10938356 \times 10^{-31} \text{ kg}$

Substituting into the energy formula:

$E = (2 \times 9.10938356 \times 10^{-31}) \times (3 \times 10^{8})^2 \approx 1.637 \times 10^{-13} \text{ J}$

Using the relationship between energy and frequency:

$E = hf$

where $h$ is Planck's constant ($6.62607015 \times 10^{-34} ext{ Js}$), we can rearrange to find:

$f = \frac{E}{h}$

Substituting the calculated energy:

$f \approx \frac{1.637 \times 10^{-13}}{6.62607015 \times 10^{-34}} \approx 2.47 \times 10^{20} \text{ Hz}$

The photons produced generally have a greater frequency due to additional energy being contributed by the motion of the colliding particles. When particles are moving, their kinetic energy converts into photon energy, resulting in photons with higher frequencies than the minimum calculated frequency.

Two positrons must travel at high speeds to ensure they have sufficient energy to overcome the repulsive electrostatic forces due to their identical positive charges. High speeds also increase their kinetic energy, enabling effective collisions to occur.

Charged particles can be accelerated using various methods such as linear accelerators, cyclotrons, synchrotrons, and magnetic fields. These technologies apply electric and magnetic forces to impart energy to the charged particles, increasing their velocities significantly.

Two positrons cannot annihilate each other because annihilation requires a particle-antiparticle pair, specifically an electron and a positron. Since both are positrons, there is no electron involved in the interaction to facilitate annihilation, as both carry positive charge and do not account for charge cancellation.