How is energy conserved in radioactive decay processes?

Energy is conserved in radioactive decay processes through the conservation of mass-energy equivalence.

In radioactive decay, an unstable nucleus transforms into a more stable one, releasing energy in the process. This energy is conserved according to the principle of mass-energy equivalence, famously encapsulated in Einstein's equation E=mc^2. This equation states that energy (E) is equal to mass (m) times the speed of light (c) squared. In other words, mass can be converted into energy and vice versa.

During radioactive decay, the total mass of the decay products (the daughter nucleus and the emitted particles) is less than the mass of the original, parent nucleus. This 'missing' mass has been converted into energy, which is carried away by the emitted particles. This energy can be in the form of kinetic energy of the particles, or as electromagnetic radiation. The total energy before and after the decay remains the same, thus conserving energy.

For example, in alpha decay, a parent nucleus emits an alpha particle (consisting of 2 protons and 2 neutrons). The mass of the parent nucleus is greater than the combined mass of the daughter nucleus and the alpha particle. The difference in mass is converted into energy, which is carried away by the alpha particle as kinetic energy. Similarly, in beta decay, a neutron in the parent nucleus transforms into a proton, emitting an electron (beta particle) and an electron antineutrino. The total energy (mass-energy of the particles plus their kinetic energy) remains the same before and after the decay.

In gamma decay, the parent nucleus is in an excited state with excess energy. It releases this energy by emitting a gamma photon, transitioning to a lower energy state. The energy of the gamma photon equals the energy difference between the initial and final states of the nucleus. Again, the total energy is conserved.

In summary, energy conservation in radioactive decay is achieved through the conversion of mass into energy, in accordance with the principle of mass-energy equivalence. The energy released in the decay process is carried away by the emitted particles or radiation, ensuring that the total energy remains constant.