Carbon-14 decays into nitrogen-14 with the release of a beta ($\beta^-$) particle and an antineutrino ($ar{ u}_e$) - AQA - A-Level Physics - Question 2 - 2022 - Paper 1

Figure 2 shows a distribution of kinetic energies of $\beta^-$ particles that indicates they have a range of energies. The presence of an antineutrino is suggested because there should be more energy observed in the decay than what is accounted for by the $\beta^-$ particle and the nitrogen-14 produced. The missing energy, evidenced by the observed spectrum, implies that another particle (the antineutrino) carries away this excess energy.

Particle X is a neutron.

The minimum energy produced in the annihilation of the positron and the electron is calculated to be $E = 2 \times 0.51 \text{ MeV} = 1.02 \text{ MeV}$. Therefore, the gamma photons produced during annihilation must each have energies of at least $1.02 \text{ MeV}$. Referring to Table 1, only gamma photons G2 ($6.6 \times 10^{-14} ext{ J}$) and G3 ($1.0 \times 10^{-13} ext{ J}$) meet this criterion.