The pair annihilation of an electron and a positron has been investigated for many years at CERN in Switzerland - Leaving Cert Physics - Question d - 2016

Photons are always produced in pairs to conserve momentum. This principle ensures that the total momentum before and after the annihilation remains zero.

The equation for pair annihilation can be represented as: $e^- + e^+ \rightarrow 2\gamma$ where $e^-$ is the electron, $e^+$ is the positron, and $\gamma$ represents the gamma-ray photon.

To find the frequency of the gamma-rays, we use the equation relating energy to frequency: $E = hf$

Given: $E = 8.1 \times 10^{-14} \text{ J}$ and Planck’s constant $h = 6.626 \times 10^{-34} \text{ J·s}$, we can rearrange to find frequency: $f = \frac{E}{h} = \frac{8.1 \times 10^{-14}}{6.626 \times 10^{-34}} \approx 1.22 \times 10^{20} \text{ Hz}$.

The energy produced in proton-antiproton annihilation is greater than that in electron-positron annihilation because the mass of the proton is greater than that of the electron. Thus, when they annihilate, more energy is released due to the equivalence of mass and energy described by Einstein's equation, $E = mc^2$.

The labelled diagram of a d.c. motor should include:

• Coil
• Magnet
• Power Supply
• Carbon Brushes
• Commutator

When current flows through the coil, it generates a magnetic field around the coil which interacts with the external magnetic field provided by the magnets. According to the motor effect, a force is exerted on each side of the coil, causing it to rotate. The commutator ensures that the direction of current (and hence the magnetic field) alternates as the coil turns, keeping it in motion.

To demonstrate the principle of operation of an induction motor, I would:

1. Use a simple setup including an induction motor and a power source.
2. Show how alternating current creates a rotating magnetic field in the stator, which induces movement in the rotor.
3. Observe the rotor turning due to the interaction between the rotating magnetic field and the rotor currents.

An advantage of an induction motor over a d.c. motor is that induction motors do not have brushes, eliminating the need for replacement and reducing maintenance.